Question

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

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