Permutations And Combinations Question 178
The number of ways of choosing a committee of two women and three men from five women and six men. If Mr. A refuses to serve on the committee if Mr. B is a member and Mr. B can only serve if Miss C is a member of the committee is
Options:
A) 60
B) 84
C) 124
D) none of these
Correct Answer: C $ \Rightarrow $ B does not come $ {{\Rightarrow }^{4}}C_2{{\times }^{5}}C_3=60 $ $ \Rightarrow $ Total=124
Alternate method:
Case I:
Mr. B is present $ \Rightarrow $ A is excluded and C included
Hence, the number of ways is $ ^{4}C_2 \times ^{4}C_1 = 24 $ .
Case II:
Mr. ‘B’ is absent $ \Rightarrow $ No constraint
Hence, the number of ways is $ ^{5}C_3 \times ^{5}C_2 $ =100. $ \therefore $ Total = 124.
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BETA
