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12 December, 08:18

17. Evaluate. Show your work.

a. 6!

b. 6P5 (little 6, capital p, little 5)

c. 12C3 (little 12, capital C, little 3)

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Answers (1)
  1. 12 December, 08:23
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    A. The factorial symbol n! indicates the product of all positive integers from 1 to n.

    Therefore:

    6! = 1 x 2 x 3 x 4 x 5 x 6 = 720

    B. The formula for permutation is:

    P = n! / (n - r) !

    The given value is 6P5 which is the form nPr. Therefore,

    P = 6! / (6 - 5) !

    P = 720 / 1

    P = 720

    C. The formula for combination is:

    C = n! / r! (n - r) !

    The given value is 12C3 which is the form nCr. Therefore,

    C = 12! / 3! (12 - 3) !

    C = 12! / 3! 9!

    Where 12! can be written as 12! = 9! x 10 x 11 x 12

    C = 9! (10 x 11 x 12) / 3! 9!

    Cancelling 9!:

    C = 10 x 11 x 12 / 3!

    C = 1,320 / 6

    C = 220
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