In how many ways can 5 boys and 4 girls be seated on a bench so that the girls and the boys occupy alternate seats?​

Question

In how many ways can 5 boys and 4 girls be seated on a bench so that the girls and the boys occupy alternate seats?​

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Latifah 4 years 2021-08-09T07:08:44+00:00 1 Answers 247 views 0

Answers ( )

  1. Sigrid
    0
    2021-08-09T07:10:07+00:00
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    Answer:

    2880 ways

    Step-by-step explanation:

    There can be only one arrangement in which boys and girls can sit.

    G-B-G-B-G-B-G-B-G

    but position of individual boy and girls can be changed.

    So, there are 5 girls and 5 slots for them that means they can be arranged in 5! ways,

    similarly boys have 4 slots, so they can be arranged in 4! ways.

    now, one more thing to consider is that out of 5! arrangements of girls, with each arrangement boys can be arranged in 4! different positions.

    so to get the total number of boys and girls arrangements together we would need to multiply the arrangements of both boys and girls.

    so the desired answer would be: 5!*4! = 120*24 = 2880 ways.

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