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?
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
