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There are 15 people in a committee. How many ways are there to group these 15 people into 3, 5, and 4?

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There are 15 people in a committee. How many ways are there to group these 15 people into 3, 5, and 4?

(a) 846

(b) 2468

(c) 658

(d) 1317

This question was posed to me during an interview for a job.

My question is taken from Counting topic in chapter Counting of Discrete Mathematics

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The correct choice is (d) 1317

The explanation is: The number of ways to choose 3 people out of 9 is ^15C3. Then, number of ways to choose 5 people out of (15-3) = 12 is ^12C5. Finally, the number of ways to choose 4 people out of (12-4) = 8 is ^8C4. Hence, by the rule of product, ^15C3 + ^12C5 + ^8C4 = 1317.

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