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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) 1317This question was posed to me during an interview for a job.My question is taken from Counting topic in chapter Counting of Discrete Mathematics

Answer»

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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