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28 March, 06:04

Compute the permutations and combinations. A company has 10 men qualified to run a machine that requires 3 operators at a time. Find how many groups of 3 operators are possible. 240 720 120

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  1. 28 March, 09:04
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    120

    Step-by-step explanation:

    To solve this question we would be using combination formula.

    The formula for combination is given as:

    C (n, r) = nCr

    nCr = n!/r! * (n - r) !

    In the above question,

    n = 10 men

    r = 3 operators

    Hence,

    nCr = n!/r! * (n - r) !

    10C3 = 10! / 3! * (10 - 3) !

    10C3 = 10!/3! * 7!

    10C3 = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / (3 * 2 * 1) * (7 * 6 * 5 * 4 * 3 * 2 * 1)

    10C3 = 10 * 9 * 8 / 3 * 2 * 1

    10C3 = 720/6

    10C3 = 120

    Therefore, the number of groups of 3 operators that are possible is 120.
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