SATHEE: Permutations And Combinations Question 316

Permutations And Combinations Question 316

Question: A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is:

Options:

A) 40

B) 41

C) 16

D) 32

Show Answer

Answer:

Correct Answer: B

Solution:

[b] Require number of ways $ {{=}^{2}}C_1{{\times }^{2}}C_1{{\times }^{4}}C_2{{+}^{2}}C_1{{\times }^{2}}C_2{{\times }^{4}}C_1 $ $ {{+}^{2}}C_2{{\times }^{2}}C_1{{\times }^{4}}C_1{{+}^{2}}C_2{{\times }^{2}}C_2{{\times }^{4}}C_0 $ $ =2\times 2\times \frac{4\times 3}{2}+2\times 1\times 4+1\times 2\times 4+1\times 1\times 1 $ $ =24+8+8+1=41 $

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Permutations And Combinations Question 316

Question: A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is:

Options:

Answer:

Solution:

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