CRE 8 - Selecting books from a shelf | Modern Math - Permutation & Combination
Answer the next 2 questions based on the information given below:
On a library shelf, there are 5 different books for Maths, 4 different books for Reasoning & 3 different books for English. In how many ways can a person select
A book from the shelf?
Answer: 12
Explanation :
There is a total of 5 + 4 + 3 = 12 different books on the shelf.
We have to pick one book.
∴ Number of ways of picking a book = 12C1 = 12 ways.
Hence, 12.
Workspace:
At least one book from the shelf?
Answer: 4095
Explanation :
There is a total of 5 + 4 + 3 = 12 different books on the shelf.
We have to pick at least book. Let us name these books as
Maths: M1, M2, M3, M4 and M5.
Reasoning: R1, R2, R3 and R4.
English: E1, E2 and E3.
There are two possibilities for each of these books i.e., either the book will be picked or not picked.
∴ Total possibilities for picking books = 212.
Now out of these 212 possibilities, there would be one possibility when no book is picked.
∴ Number of ways of picking at least 1 book = 212 - 1 = 4096 – 1 = 4095 ways.
Hence, 4095.
Workspace:
At least one book on each subject from the shelf?
Answer: 3255
Explanation :
There is a total of 5 + 4 + 3 = 12 different books on the shelf.
We have to pick at least book. Let us name these books as
Maths: M1, M2, M3, M4 and M5.
Reasoning: R1, R2, R3 and R4.
English: E1, E2 and E3.
There are two possibilities for each of the Maths i.e., either the book will be picked or not picked.
∴ Total possibilities for picking Maths books = 25.
Now out of these 25 possibilities, there would be one possibility when no book is picked.
∴ Number of ways of picking at least 1 Maths book = 25 – 1.
Similarly,
Number of ways of picking at least 1 Reasoning book = 24 – 1, and
Number of ways of picking at least 1 English book = 23 – 1.
∴ Number of ways of picking at least 1 book of each subject = (25 – 1) × (24 – 1) × (23 – 1) = 31 × 15 × 7 = 3255.
Hence, 3255.
Workspace:
Answer the next 2 questions based on the information given below:
On a library shelf, there are 5 identical books for Maths, 4 identical books for Reasoning & 3 identical books for English. In how many ways can a person select
A book from the shelf?
Answer: 3
Explanation :
There are 5 identical Maths books, 4 identical Reasoning books and 3 identical English books.
We have to pick 1 book, now this book can either be a Math book or Reasoning book or an English book i.e., 3 ways.
Hence, 3.
Workspace:
At least one book from the shelf?
Answer: 119
Explanation :
There are 5 identical Maths books, 4 identical Reasoning books and 3 identical English books.
For Math books:
Either we can pick no Math book or only 1 book or 2 books or 3 books or 4 books or 5 books i.e., we can pick Math books in (5 + 1) = 6 ways.
Similarly for Reasoning, number of ways of picking books = (4 + 1) = 5 ways, and
For English, number of ways of picking books = (3 + 1) = 4 ways.
∴ Total Number of ways of picking books = (5 + 1)(4 + 1)(3 + 1) = 120 ways.
Out of these 120 ways, there would be 1 possibility when no book is picked.
∴ Total Number of ways of picking at least 1 book = 120 – 1 = 119 ways.
Hence, 119.
Workspace:
At least one book on each subject from the shelf?
Answer: 60
Explanation :
There are 5 identical Maths books, 4 identical Reasoning books and 3 identical English books.
For Math books:
Either we can pick only 1 book or 2 books or 3 books or 4 books or 5 books i.e., we can pick Math books in 5 ways.
Similarly for Reasoning, number of ways of picking books = 4 ways, and
For English, number of ways of picking books = 3 ways.
∴ Total Number of ways of picking at least one book of each subject = 5 × 4 × 3 = 60 ways.
Hence, 60.
Workspace:
Feedback
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.