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19 July, 19:27

Three research departments have 8,6,7 members, respectively. Each department is to select a delegate and an alternate to represent the department at a conference. In how many ways can this be done

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  1. 19 July, 21:33
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    70,560 ways

    Step-by-step explanation:

    This problem is an arrangement problem, as the order of the two people chose in each department matters.

    So, for each department, we have an arrangement:

    First department: arrange of 8 choose 2: A (8,2) = 8!/2! = 8*7 = 56

    Second department: arrange of 6 choose 2: A (6,2) = 6!/2! = 6*5 = 30

    Third department: arrange of 7 choose 2: A (7,2) = 7!/2! = 7*6 = 42

    The total number of ways is the product of each number of arranges, so:

    Number of ways = 56 * 30 * 42 = 70,560
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