Why is the answer to the following problem 3960 rather than 8580

Question

The question: In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

Now, as per my understanding, we need to select four bowlers from the pool of five players who can bowl. But this does not mean that the fifth person i.e the reject cannot be on the rest of the team?

My answer: $^5C_4*^{13}C_7 = 5*1716$

The book: $^5C_4*^{12}C_7 = 5*792$

Which one is correct?

If you choose from $13$ players, you could be selecting a fifth bowler. — N. F. Taussig, Feb 15 '16 at 16:33
It is a matter of interpretation. You interpreted the question one way, the solver interpreted the question in another way. — André Nicolas, Feb 15 '16 at 16:38

score 1 · Accepted Answer · answered Feb 15 '16 at 16:33

1

Here, can bowl means is a bowler. As the question asks for exactly four bowlers, the fifth cannot be a part of the team. The solution in the book is correct.

answered Feb 15 '16 at 16:33

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Why is the answer to the following problem 3960 rather than 8580

1 Answers1