Question

1. The Mathematics Department at Sun Tan University is sending a delegation of mathematicians and graduate students to a conference. They will pay for 4 mathematicians and 5 graduate students to go. If the department has 16 mathematicians and 24 graduate students, how many different delegations are possible?

Answer 1

The delegation consists of a combination of 4 mathematicians and 5 graduate students.

16C4 * 24C5
= [16! / (12! 4!)] [24! / (19! 5!)]
= 16! 24! / (12! 4! 19! 5!)
= 16*15*14*13 * 24*23*22*21*20 / (24 * 120)
= 23*22*21*20 * 16*15*14*13 / 120
= 77,357,280 delegations possible

Answer 2

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