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26 January, 07:47

Samantha must include 1 English class, 1 Algebra class, and 1 Biology class in a schedule. There 3 English teachers, 4 Algebra teachers, and 2 Biology teachers. How many different schedules are possible?

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  1. 26 January, 07:49
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    To solve this problem, we make use of the formula of combination.

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

    where n is the total number of subject teachers and r is the number of subjects r = 1

    For the English class n = 3

    3C1 = 3! / 1! (3 - 1) ! = 3

    For the Algebra class n = 4

    4C1 = 4! / 1! (4 - 1) ! = 4

    For the Biology class n = 2

    2C1 = 2! / 1! (2 - 1) ! = 2

    The total number of different schedules would be the product of the three combinations:

    total combinations possible = 3 * 4 * 2

    total combinations possible = 24
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