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.
(i) 10! = 3628800
total no. of ways = 5C1 x 8! x 4C1
total no. of ways = 2C2 x 8C2 x 2! x 2! x 6C6 x 6!
note: 2! x 2! is the number of ways of arranging the teachers.
7C3 x 3! x 6! x 2! = 302400
note: 3! = choosing empty seats for groups of 3
2! = arranging 2 teachers