Permutation of groups into rows 2

A class committee consists of 5 boys, 3 girls and 2 teachers. They have to take a group photograph for the school magazine. Find the number of ways they can be arranged.

(i) in a row without any restriction

(ii) in a row such that there is a boy at each end of the row

(iii) in 2 rows, with 4 people in the fist row, such that the 2 teachers

(iv) in a row such that the 2 teachers are together and no 2 girls are next to each other.

Solution

(i) 10! = 3628800

(ii) 806400

total no. of ways = 5C1 x 8! x 4C1

                                = 806400

(iii) 80640

total no. of ways = 2C2 x 8C2 x 2! x 2! x 6C6 x 6!

                                =80640

note: 2! x 2! is the number of ways of arranging the teachers.

(iv) 302400

7C3 x 3! x 6! x 2! = 302400

note: 3! = choosing empty seats for groups of 3

         2! = arranging 2 teachers

 

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