7. There are seven clarinet players in the concert band. In how many ways can they be seated in seven chairs at a concert? Use the

Question

7. There are seven clarinet players in the concert band. In how
many ways can they be seated in seven chairs at a concert?
Use the Fundamental Counting Principle.

A. 5,040
C. 840
B. 2,520
D. 210​

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Ella 1 month 2021-10-15T03:30:36+00:00 1 Answer 0 views 0

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    2021-10-15T03:31:54+00:00

    Answer:

    5,040

    Step-by-step explanation:

    Fundamental Counting Principle states that if there are m ways of doing a thing and there are n ways of doing other thing  then there are total m*n ways of doing both things.

    Example : If there are 5 path to reach a destination and 3 mode of transport ( bike, car, bicycle) . Then are 5 * 3 ways to reach the destination using the different mode of transport available.

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    Given no of clarinet players = 7

    no of chairs = 7

    First player can be seated on seven chairs in seven ways

    ( for illustration let the seat be a , b, c , d , e , f , g. he can sit on any of the chairs)

    since one chair is occupied and 6 chair is available

    second player can be seated on 6 chairs in 6 ways

    for illustration let the seat be a be occupied then b, c , d , e , f , g are  the chairs on which second player can sit.

    \

    Similarly 3rd, 4th, 5th, 6th and 7th player can be seat on chairs in

    5, 4 , 3, 2, and 1 way respectively.

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    now using  fundamental Counting Principle

    since 7 players can sit on chair in

    7 , 6, 5 , 4, 3 , 2, 1 ways then together they can be seated in

    7 *  6 * 5 *  4 * 3 * 2 * 1 ways = 5, 040 ways

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