Modern Math - Permutation & Combination - Previous Year CAT/MBA Questions
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4. IIFT 05 Dec 2021 QA | Modern Math - Permutation & Combination omet Question
How many 4 letter words can be formed from the word "CORONAVIRUS"
- (a)
3148
- (b)
3058
- (c)
3702
- (d)
3086
Answer: Option
C
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Text Explanation :
"CORONAVIRUS" has 7 distinct alphabets and two pairs of repeated characters ", O" and "R".
There are three possible cases for creating 4 letter words.
1. Two letters are "O" and the other two are "R".
The total number of arrangements = = 6
2. Two of the letters are either "O" or "R" and the others are distinct.
The total number of arrangements = 2C1 × 8C2 × = 2 × 28 × 12 = 672
3. All four letters are distinct.
The total number of arrangements = 6C4 × 4! = 3024
Thus, the total number of four-letter words possible = 6 + 672 + 3024 = 3702.
Hence, the answer is option C.
5. IIFT 2020 QA | Modern Math - Permutation & Combination omet Question
Refer to the figure given below. AB, CD and EF are three parallel paths. A person starts from AB to reach EF by moving in four steps - moving from AB to O1 in step 1, from O1 to CD in step 2, from CD to O2 in step 3 and from O2 to EF in step 4. If he takes a curved path in one step, he cannot take a curved path in the next step. In how many ways the person can reach EF from AB?
- (a)
128
- (b)
256
- (c)
32
- (d)
64
Answer: Option
A
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Text Explanation :
The total number of possible ways from AB to EF = 4 × 4 × 4 × 4 = 256
If a curved path is taken in a step, then the next step cannot be a curved path.
Let C denotes a curved path and S denotes a straight path.
Thus, the invalid paths are as follows: CCCC, CCCS, CCSC, CSCC, SCCC, CCSS, SCCS, SSCC. Thus, a total of 8 paths.
Total number of arrangements for these 8 paths = 8 × 2 × 2 × 2 × 2 = 128
Thus, the total number of valid paths = 256 - 128 = 128
Hence, the answer is option A.
6. XAT 2019 QADI | Modern Math - Permutation & Combination omet Question
A bag contains marbles of three colours-red, blue and green. There are 8 blue marbles in the bag. There are two additional statement of facts available:
- If we pull out marbles from the bag at random, to guarantee that we have at least 3 green marbles, we need to extract 17 marbles.
- If we pull out marbles from the bag at random, to guarantee that we have at least 2 red marbles, we need to extract 19 marbles.
Which of the two statements above, alone or in combination shall be sufficient to answer the question "how many green marbles are there in the bag"?
- (a)
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
- (b)
Each statement alone is sufficient to answer the question.
- (c)
Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question.
- (d)
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
- (e)
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
Answer: Option
D
Video Explanation
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Text Explanation :
We know that in all there are 8 blue marbles.
Let us first look at statement I.
As per statement I if we are to pull out 17 marbles from the bag, we will ensure that there are at least 3 greeen marbles. Now out of 17 marbles removed, 8 are blue .So from the 9 marbles that are removed, if at least 3 are green, it would mean maximum possible no of red marbles removed are 9-3 or 6.Which means that the red marbles in the bag are 6.However, this statement alone gives us no information about the no of green marbles. Hence statement I alone is not sufficient to answer the question.
Let us next look at statement II.
As per this statement, if we are to pull out 19 marbles from the bag, we would have at least 2 red marbles. Out of the 19 marbles removed, suppose 8 are blue. Now out of the remaining 11 marbles removed, if we have at least 2 red marbles, it would mean that the maximum possible no of green marbles removed is 9.This means that in all there are 9 green marbles in the bag .
Hence statement 2 alone is sufficient to answer the question.
Hence, option (d).
7. IIFT 2019 QA | Modern Math - Permutation & Combination omet Question
Four couples are to be seated in a circular table such that each couple sits together. In how many ways they can sit such that two males sit to the right of their female partners and the other two males sit to the left of their female partners?
- (a)
144
- (b)
288
- (c)
1440
- (d)
720
Answer: Option
B
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Text Explanation :
First of all, we will have to select 2 couples where the male sits to the right of the female in 4C2 = 6 ways (and the other two couples select them automatically)
Now, we can fix anyone of the couple in 4 ways and in these couples, females may be seated to the left/right of the males
Total ways of fixing a couple = 8
The other three couples can be arranged in 3! ways = 6 ways
∴ Total number of ways = 6 × 8 × 8 = 288
Hence, option (b).
8. IIFT 2018 QA | Modern Math - Permutation & Combination omet Question
P . . . . . Q
R . . . . . S
T . . . . . U
V . . . . . W
Using 5 dots in each of the lines PQ, RS, TU and VW as the vertices, how many triangles can be drawn such that the base is on any one of the above lines?
- (a)
120
- (b)
150
- (c)
200
- (d)
600
Answer: Option
D
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Text Explanation :
The base has to be on one of the four lines.
Hence, the base can first be chosen in 4 ways.
Now, on this base, two points need to chosen from five to form the actual base. This can be done in 5C2 ways i.e. 10 ways
For the third point, one of three lines has to be chosen and then one of five points from each line has to be chosen.
∴ Number of possible triangles = 4 × 10 × 3 × 5 = 600
Hence, option (d).
9. IIFT 2016 QA | Modern Math - Permutation & Combination omet Question
A playschool contains 4 boys and y girls. On every Wednesday during winter, five students, of which at least three are boys, go to Zoological Garden, a different group being sent every week. At the Zoological Garden, each boy in the group is given a ball. If the total number of balls distributed is 368, then the value of y is
Answer: Option
D
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Text Explanation :
Since the group has to have atleast three boys, number of ways in which a group of five can be formed = (4C3 × yC2) + (4C4 × yC1) = [4 × (y)(y – 1)/2] + [(1)(y)] = 2y(y – 1) + y
Since each boy in the group gets a ball, total balls distributed = 3[2y(y – 1)] + 4y = 6y2 – 2y
Since total balls distributed= 368; 6y2 – 2y = 368
∴ 3y2 – y – 184 = 0
On solving this, y = 8
Hence, option (d).
10. IIFT 2016 QA | Modern Math - Permutation & Combination omet Question
Which of the following statements regarding arrangement of the word ‘RIYADH’ is/are true:
i. Two vowels can be arranged together in 120 ways
ii. Vowels do not occur together in 240 ways
Which of the above statements are true?
Answer: Option
D
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Text Explanation :
(i) Two vowels can be arranged together in RIYADH in 5! × 2! = 240 ways
Hence, statement (i) is not true.
(ii) Total arrangements where vowels are not together = total arrangements possible – arrangements where vowels are together = 6! – 240 = 720 – 240 = 480
Hence, statement (ii) is also not true.
Hence, option (d).
11. IIFT 2016 QA | Modern Math - Permutation & Combination omet Question
A reputed paint company plans to award prizes to its top three salespersons, with the highest prize going to the top salesperson, the next highest prize to the next salesperson and a smaller prize to the third-ranking salesperson. If the company has 15 salespersons, how many different arrangements of winners are possible (Assume there are no ties)?
- (a)
1728
- (b)
2730
- (c)
3856
- (d)
1320
Answer: Option
B
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Text Explanation :
This is a case of first selecting the top three salesmen out of 15 and then arranging them as first, second and third i.e. 15P3
∴ Number of arrangements = 15C3 × 3! = 2730
Hence, option (b).
12. IIFT 2016 QA | Modern Math - Permutation & Combination omet Question
In an MBA entrance examination, a minimum is to be secured in each of the 6 sections to qualify the cut-offs. In how many ways can a candidate fail to secure the cut-offs?
- (a)
60
- (b)
61
- (c)
62
- (d)
63
Answer: Option
D
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Text Explanation :
Number of ways in which the candidate fails to secure the cut-offs in no section out of 6 sections = 6Co = 1
Number of ways in which the candidate may/may not secure the cut-offs
= 6Co+ 6C1 + 6C2 + 6C3 + 6C4 + 6C5 + 6C6
= 26 = 64
Thus, the number of ways in which he fails to secure the cut offs in at least one section = 64 − 1 = 63
Hence, option (d).
13. IIFT 2015 QA | Modern Math - Permutation & Combination omet Question
During the essay writing stage of MBA admission process in a reputed B-School, each group consists of 10 students. In one such group, two students are batchmates from the same IIT department. Assuming that the students are sitting in a row, the number of ways in which the students can sit so that the two batchmates are not sitting next to each other, is:
- (a)
3540340
- (b)
2874590
- (c)
2903040
- (d)
None of the above
Answer: Option
C
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Text Explanation :
Number of ways in which 10 students can sit = 10!
The number of ways in which two students (batchmates) sit together = 9! × 2
∴ The number of ways in which the student can sit so that the two batchmates are not sitting next to each other = 10! – 9! × 2 = 9! × 8 = 2903040
Hence, option (c).
14. IIFT 2015 QA | Modern Math - Permutation & Combination omet Question
In the board meeting of a FMCG Company, everybody present in the meeting shakes hand with everybody else. If the total number of handshakes is 78, the number of members who attended the board meeting is:
- (a)
7
- (b)
9
- (c)
11
- (d)
13
Answer: Option
D
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Text Explanation :
Let n members attended the board meeting.
Number of handshakes = n×(n – 1)/2 = 78
Solving this, n = 13
Hence, option (d).
15. IIFT 2014 QA | Modern Math - Permutation & Combination omet Question
In a school, students were called for the Flag Hoisting ceremony on August 15. After the ceremony, small boxes of sweets were distributed among the students. In each class, the student with roll no. 1 got one box of sweets, student with roll number 2 got 2 boxes of sweets, student with roll no. 3 got 3 boxes of sweets and so on. In class III, a total of 1200 boxes of sweets were distributed. By mistake one of the students of class III got double the sweets he was entitled to get. Identify the roll number of the student who got twice as many boxes of sweets as compared to his entitlement.
- (a)
22
- (b)
24
- (c)
28
- (d)
30
Answer: Option
B
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Text Explanation :
(1 + 2 + 3 + … + n) + x = 1200
Where, x is the roll number of the student who got twice as many as compared to his entitlement.
n (n + 1)/2 = 1200 – x ⇒ n (n + 1)
= 2400 – 2x
Substituting values of x from options, only for x = 24, the RHS can be expressed as a product of two natural numbers.
Hence, option (b).
16. IIFT 2014 QA | Modern Math - Permutation & Combination omet Question
In the MBA Programme of a B – School, there are two sections A and B. 1/4th of the students in Section A and 4/9th of the students in section B are girls. If two students are chosen at random, one each from section A and Section B as class representative, the probability that exactly one of the students chosen is a girl, is:
- (a)
23/72
- (b)
11/36
- (c)
5/12
- (d)
17/36
Answer: Option
D
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Text Explanation :
Selecting a girl from section A and section B is 1/4 and 4/9 respectively.
Selecting a boy from section A and section B is 3/4 and 5/9 respectively.
Case 1: A girl from section A and a boy from section B.
P1 = (1/4) × (5/9) = 5/36
Case 2: A boy from section A and a girl from section B.
P2 = (3/4) × (4/9) = 12/36
Required probability = P1 + P2 =17/36
Hence, option (d).
17. IIFT 2014 QA | Modern Math - Permutation & Combination omet Question
In an Engineering College in Pune, 8 males and 7 females have appeared for Student Cultural Committee selection process. 3 males and 4 females are to be selected. The total number of ways in which the committee can be formed, given that Mr. Raj is not to be included in the committee if Ms. Rani is selected, is:
- (a)
1960
- (b)
2840
- (c)
1540
- (d)
None of the above
Answer: Option
C
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Text Explanation :
Selecting 3 males from 8 and 4 females from 7 can be done in 8C3 × 7C4 = 56 × 35 = 1960
Raj and Rani together cannot be in the committee.
Selection of both Raj and Rani can happen in 7C2 × 6C3 = 21 × 20 = 420
Required number of ways = 1960 – 420 = 1540
Hence, option (c).
18. IIFT 2013 QA | Modern Math - Permutation & Combination omet Question
Mrs. Sonia buys Rs. 249.00 worth of candies for the children of a school. For each girl she gets a strawberry flavoured candy priced at Rs. 3.30 per candy; each boy receives a chocolate flavoured candy priced at Rs. 2.90 per candy. How many candies of each type did she buy?
- (a)
21, 57
- (b)
57, 21
- (c)
37, 51
- (d)
27, 51
Answer: Option
B
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Text Explanation :
Let the number of strawberry and chocolate flavoured candies be a and b respectively.
∴ 3.3a + 2.9b = 249
Since there is only one equation with two unknowns, substitute the given options into the equations.
By substitution, a = 57 and b = 21 satisfy the given equation.
Hence, option (b).
19. IIFT 2013 QA | Modern Math - Permutation & Combination omet Question
Out of 8 consonants and 5 vowels, how many words can be made, each containing 4 consonants and 3 vowels?
- (a)
700
- (b)
504000
- (c)
3528000
- (d)
7056000
Answer: Option
C
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Text Explanation :
Out of 8 consonants, 4 consonants can be selected in 8C4 = 70 ways.
Out of 5 vowels, 3 vowels can be selected in 5C3
= 10 ways.
These 7 selected letters can be arranged among themselves in 7! ways.
Thus total number of ways = 70 ´ 10 ´ 7! = 3528000
Hence, option (c).
20. IIFT 2013 QA | Modern Math - Permutation & Combination omet Question
In a sports meet for senior citizens organized by the Rotary Club in Kolkata, 9 married couples participated in Table Tennis mixed double event. The number of ways in which the mixed double team can be made, so that no husband and wife play in the same set, is
- (a)
1512
- (b)
1240
- (c)
960
- (d)
640
Answer: Option
A
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Text Explanation :
Two men can be selected in 9C2 ways.
After selecting two men, two women can be selected in 7C2 ways from (9 – 2 = 7) women, so that no husband and wife play in the same set.
Also, these selected 4 people can be grouped in 2 ways.
∴ The total number of mixed double teams
= 9C2 ×7C2 × 2 = 1512
Hence, option (a).
21. IIFT 2010 QA | Modern Math - Permutation & Combination omet Question
In how many ways can four letters of the word ‘SERIES’ be arranged?
- (a)
24
- (b)
42
- (c)
84
- (d)
102
Answer: Option
D
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Text Explanation :
The words SERIES has one R, one I, two Es and two Ss.
Four letters can be selected and arranged in the following ways:
∴ Total number of arrangements = 6 + 12 + 12 + 12 + 12 + 12 + 12 + 24 = 102
Hence, option (d).
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