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17 March, 13:05

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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  1. 17 March, 13:27
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    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
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