SATHEE: Permutations And Combinations Question 33

Permutations And Combinations Question 33

Question: In how many ways can a committee be formed of 5 members from 6 men and 4 women if the committee has at least one woman [RPET 1987; IIT 1968; Pb. CET 2003]

Options:

A) 186

B) 246

C) 252

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

The number of ways can be deduce as follows: 1 woman and 4 men $ {{=}^{4}}C_1{{\times }^{6}}C_4=60 $ 2 women and 3 men $ {{=}^{4}}C_2{{\times }^{6}}C_3=120 $ 3 women and 2 men $ {{=}^{4}}C_3{{\times }^{6}}C_2=60 $ 4 women and 1 man $ {{=}^{4}}C_4{{\times }^{6}}C_1=6 $ Required number of ways $ {{=}^{7}}C_4=35 $ .

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Permutations And Combinations Question 33

Question: In how many ways can a committee be formed of 5 members from 6 men and 4 women if the committee has at least one woman [RPET 1987; IIT 1968; Pb. CET 2003]

Options:

Answer:

Solution:

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