Question

How many ways are there to form a team of 7 athletes from a group of 15 who try out?

Answer 1

The number of ways to form the team is 6435.

Step-by-step explanation:

The number of ways to form the team can be determined by combination method. So that;

Number of ways =
`(n!)/(r!(n-r)!)`

where r = 7 and n = 15.

=
`(15!)/((15 - 7)!7!)`

=
`(15!)/(8!7!)`

=
`(15*14*13*12*11*10*9*8!)/(8!*7*6*5*4*3*2*1)`

=
`(15*14*13*12*11*10*9)/(7*6*5*4*3*2*1)`

=
`(32432400)/(5040)`

= 6435

The number of ways to form the team is 6435.