Question

A choir of singers is made up of 7 soprano, 5 alto, 5 tenor and 6 bass singers. In a performance, the choir will stand in two rows. In how many ways can the singers be arranged
a) if there are no restriction?
b) if sopranos and altos must be in the front row while the rest in the back row?
c) if condition in (b) applies, and each type of voice must be grouped together?

Answer 1

a) 23!

Answer 2

b) \(12!\times11!\)

Answer 3

c) 7!5!5!6!