CRE 5 - Forming a committee | Modern Math - Permutation & Combination

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Answer the next 10 questions based on the information given below:

A team of seven members is to be formed from among 7 men – A, B, C, D, E, F & G and 6 women – P, Q, R, S, T & U. In how many ways can the committee be formed such that there is/are

1. CRE 5 - Forming a committee | Modern Math - Permutation & Combination

No restrictions on team selection?

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Answer: 1716

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Explanation :

Total members available for selection = 7 + 6 = 13.

∴ 7 people are to be selected from 13, hence number of ways = ¹³C₇ = $\frac{13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7}{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}$ = 1716.

Hence, 1716.

2. CRE 5 - Forming a committee | Modern Math - Permutation & Combination

4 men & 3 women in the team?

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3. CRE 5 - Forming a committee | Modern Math - Permutation & Combination

At least 1 man in the team?

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4. CRE 5 - Forming a committee | Modern Math - Permutation & Combination

At least one person from each gender?

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5. CRE 5 - Forming a committee | Modern Math - Permutation & Combination

Women are in majority?

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6. CRE 5 - Forming a committee | Modern Math - Permutation & Combination

C is always present in any chosen committee?

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7. CRE 5 - Forming a committee | Modern Math - Permutation & Combination

F is not chosen for the committee?

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8. CRE 5 - Forming a committee | Modern Math - Permutation & Combination

P & E are not simultaneously chosen for the committee?

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9. CRE 5 - Forming a committee | Modern Math - Permutation & Combination

S is chosen, only if B is chosen for the committee?

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10. CRE 5 - Forming a committee | Modern Math - Permutation & Combination

2 women & 5 men such that B, C, & G must be chosen while none among Q, T & U must be chosen?

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CRE 5 - Forming a committee | Modern Math - Permutation & Combination

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