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25 August, 01:19

How many more ways can 10 juniors running for the positions of president, vice president, secretary, treasurer be selected when compared to 12 sophomores running for 5 identical positions of class representative's?

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  1. 25 August, 01:40
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    10 juniors are running for 4 positions.

    There are ten people who can get into the first spot

    Nine people for the second

    8 people for the third

    7 for the fourth

    10x9x8x7 = 5040 different ways.

    For the sophomores: 12x11x10x9x8 = 95040

    However, the positions are identical which means that the order doesn't matter. (There's a difference between A getting postion 1, B for 2, C for 3, D for 4 and B for 1, A for 2, C for 3, D for 4)

    There are 5 identical positions, therefore we divide this by 5! (5x4x3x2x1) = 120

    95040/120 = 792

    Juniors have 5040 positions, sophomores have 792
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