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Help with the following JEE math question from http://www.trueshelf.com \n\n A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is \n\n (A) 360 \n (B) 320 \n (C) 260 \n (D) 95
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ARG
2
I am familiar with how to figure out number of possible combinations and it seems within my reach to understand. I don't know how to even start working on this problem.
Frank T
2
There are two possible ways a team can be formed, either with only one boy or with no boys (at most one boy means \geq 1 boy)Therefore we can find the number of ways with one boy: ^4 C_1 \times ^6C_3 , and with no boys: ^6C_4 . Adding the two sets of possible teams results in 95. HOWEVER we must also account for all the possible captain selections. Multiplying by 4 accomplishes this and we have 380 for the final answer. Although this is not included in your answer options I am quite confident it is correct.