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*