An NFL coach sometimes uses a defense that utilizes 3 defensive linemen, 4 linebackers, and 4 defensive backs. His roster (the players he ca

Question

An NFL coach sometimes uses a defense that utilizes 3 defensive linemen, 4 linebackers, and 4 defensive backs. His roster (the players he can choose from) includes 8 defensive linemen, 7 linebackers, and 7 defensive backs.

How many different ways can the coach pick the 11 players to implement this particular defense? _________

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Luna 2 weeks 2021-09-11T22:54:00+00:00 1 Answer 0

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    2021-09-11T22:55:17+00:00

    Answer:

    68,600

    Step-by-step explanation:

    The order of the players is not important. For example, a defensive line of Shaq Lawson, Ed Oliver and Jerry Hughes is the same as a defensive line of Ed Oliver, Shaq Lawson and Jerry Hughes. So we use the combinations formula to solve this question.

    Combinations formula:

    C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

    C_{n,x} = \frac{n!}{x!(n-x)!}

    Defensive Lineman:

    3 from a set of 8. So

    C_{8,3} = \frac{8!}{3!5!} = 56

    56 combinations of defensive lineman

    Linebackers:

    4 from a set of 7. So

    C_{7,4} = \frac{7!}{4!3!} = 35

    35 combinations of linebackers

    Defensive backs:

    4 from a set of 7. So

    C_{7,4} = \frac{7!}{4!3!} = 35

    35 combinations of defensive backs

    How many different ways can the coach pick the 11 players to implement this particular defense?

    56*35*35 = 68,600

    68,600 different ways can the coach pick the 11 players to implement this particular defense

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45:7+7-4:2-5:5*4+35:2 =? ( )