SATHEE: Permutations And Combinations Question 314

Permutations And Combinations Question 314

Question: Four couples (husband and wife) decide to form a committee of four members. Find the number of different committees that can be formed in which no couple finds a place.

Options:

A) 12

B) 14

C) 16

D) 24

Show Answer

Answer:

Correct Answer: C

Solution:

[c] The number of committees of 4 gentlemen $ {{=}^{4}}C_4=1 $ The number of committees of 3 gentlemen, 1 wife $ {{=}^{4}}C_3{{\times }^{1}}C_1 $ ( $ \because $ After selecting 3 gentlemen only 1 wife is left who can be included) The number of committees of 2 gentlemen, 2 wives $ {{=}^{4}}C_2{{\times }^{2}}C_2 $ The number of committees of 1 gentleman, 3 wives $ {{=}^{4}}C_1{{\times }^{3}}C_3 $ The number of committees of 4 wives = 1
$ \therefore $ The required number of committees $ =1+4+6+4+1=16 $

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Permutations And Combinations Question 314

Question: Four couples (husband and wife) decide to form a committee of four members. Find the number of different committees that can be formed in which no couple finds a place.

Options:

Answer:

Solution:

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