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21 April, 14:44

A group of four boys (Alex, Bryan, Chris, and David) and five girls (Megan, Nancy, Olivia, Pauline, and Rebecc?

A group of four boys (Alex, Bryan, Chris, and David) and five girls (Megan, Nancy, Olivia, Pauline, and Rebecca) are going to sit together in a row of 9 theater seats.

(a) In how many ways can they seat themselves?

(b) In how many ways can they seat themselves if the boys all sit together and the girls

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  1. 21 April, 15:07
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    a) P = 362880 ways

    b) P = 2880 ways

    Step-by-step explanation:

    a) We have four boys and five girls, they are going to sit together in a row of 9 theater seats, without restrictions

    We have a permutation of 9 elements

    P = 9!

    P = 9*8*7*6*5*4*3*2*1

    P = 362880 ways

    b) Boys must seat together, we have two groups of people

    4 boys they can seat in 4! different ways

    P₁ = 4!

    P₁ = 4*3*2*1

    P₁ = 24

    And girls can seat in 5! dfferent ways

    P₂ = 5!

    P₂ = 5*4*3*2*1

    P₂ = 120

    To get total ways in the above mentioned condition, we have to multiply P₁*P₂

    P = 24*120

    P = 2880 ways
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