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27 April, 04:56

Three research department is have 10 seven and eight members respectively each department is to select a delicate in an alternate to represent the department at a conference in how many ways can this be done

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  1. 27 April, 05:24
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    We conclude that exists 211680 ways.

    Step-by-step explanation:

    We know that the three research department is have 10, 7 and 8 members.

    We choose a delegate and an alternate to represent the department.

    First case: department have 10 members.

    So, for a delegate, we have 10 options, and for a alternate 9, so a total of

    10 * 9 = 90 options.

    Second case: department have 7 members.

    So, for a delegate, we have 7 options, and for a alternate 6, so a total of

    7 * 6 = 42 options.

    Third case: department have 8 members.

    So, for a delegate, we have 8 options, and for a alternate 7, so a total of

    8 * 7 = 56 options.

    Therefore, we get:

    90 · 42 · 56 = 211680

    We conclude that exists 211680 ways.
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