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?

Question

Mathematics

Cristopher Li

13 May, 00:48

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?

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Hugo Jones · Answer 1

Since order does not matter, we use combinations to find the total number of delegations.

We have 4 out of 16 mathematicians: 16C4

And 5 out of 24 graduate students: 24C5

Multiplying: 16C4 x 24C5

= 16! / (12!4!) * 24! / (19!5!)

= (16*15*14*13) / (4*3*2) * (24*23*22*21*20) / (5*4*3*2)

= 77,357,280 delegations