A two member committee comprising of one male and one female member is to be constituted out of five males and three females. Amongst the females. Ms. A refuses to be a member of the committee in which Mr. B is taken as the member. In how many different w

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Q: 69 (IAS/2003)
A two member committee comprising of one male and one female member is to be constituted out of five males and three females. Amongst the females. Ms. A refuses to be a member of the committee in which Mr. B is taken as the member. In how many different ways can the committee be constituted?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,1,5,1,3,1,1

keywords: 

{'member committee comprising': [0, 0, 1, 0], 'committee': [0, 0, 0, 1], 'female member': [0, 0, 1, 0], 'males': [0, 0, 0, 1], 'member': [22, 5, 20, 36], 'females': [4, 3, 4, 1], 'many different ways': [0, 0, 8, 0], 'male': [2, 0, 2, 1]}

Option 1: If we considered Ms. A and Mr. B in the committee, then there would be less possible combinations. However, since Ms. A refuses to be in a committee with Mr. B, this option is invalid.

Option 2: If we had only 12 possible combinations, that would mean either some of the females or males are not considered. Since Ms. A and Mr. B can`t be in the same committee and there are 5 males and 3 females, we expect more than 12 combinations.

Option 3: Similarly to option 2, with 13 possible combinations some potential combinations are left out which would mean not all of the females and males are considered.

Option 4: There are 5 males and since Ms. A won`t team with Mr. B, there are 2 other females that could. So combinations considering other males are 5*2=10. The combination of Ms. A with the remaining 4 males gives us another 4 possibilities. So, total possible combinations are 10+4=14. Hence, correct answer is 14.