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
Correct Answer: B The number of ways can be deduced 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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Answer:
Solution:
BETA
