If the police have 9 suspects how many different ways can they select 5 for a lineup

Assuming the order does not matter, you want the number of combinations of 9 things taken 5 at a time. The combinations can be shown as C (9,5), 9C5.

C (9, 5) =

9/5 (9-5) =

9*8*7*6*5 / 5*4

The 5 terms cancel.

9*8*7*6 / 4*3*2 =

9*7*2 =

126

The above change is because 4*2 cancels the 8 in the numerator and 6/3 = 2

Therefore, the solution is 126.