An English class consists of 22 students, and five are to be chosen to give speeches.

Question

An English class consists of 22 students, and five are to be chosen to give speeches in a school competition. In how many different ways can the teacher choose the team, given the following conditions?

(a) The order of the speakers is important.

 

(b) The order of the speakers is not important.

 

Answer 1

b) if order doesn't matter then number of

ways of choosing 5 of 22 = 22C5 = 22!/5!17! = 22x21x20x19x18/5x4x3x2 = 11x7x19x18=209x7x18=1463x18= 29,260-2,926

= 26,334

a) if order matters then ways =22P5=5!(22C5)=22!/17!

=22x21x20x19x18=26,334(5!)=26,334x5x4x3x2=26,334x120=2,633,400+526,680=

3,160,080