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 front row while the rest in the back row
c) if the condition in (b) applies, and each type of voice must be grouped together

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 front row while the rest in the back row
c) if the condition in (b) applies, and each type of voice must be grouped together

campbell_st · Answer

(a) 23!

(b) 11! x 12!         Back row (5 tenors + 6 bass = 11) front row (7 sopranos + 5 altos = 12)

(c) Back row   5! x 6! x 2!  front row 7! x 5! x 2!         2! ways of arranging 2 objects in a row

then the number of arrangements is 

5! x 6! x2! x 7! x 5! x2!