If the police have 8 suspects, how many different ways can they select 5 for a lineup?

56 different ways

Step-by-step explanation:

This is a combination question since it deals with selection. For example, if n objects is to be selected from a pool of r objects, this can be done in nCr different ways.

nCr = n!/(n-r)!r!

According to the question, If the police have 8 suspects, the different number of ways 5 can be selected for a line up is expressed as 8C5

8C5 = 8!/(8-5)!5!

8C5 = 8!/(3!)!5!

8C5 = 8*7*6*5!/3*2*5!

8C5 = 8*7*6/3*2

8C5 = 8*7

8C5 = 56 different ways

Hence, the selection of picking 5 for a line up out of 8 suspects can be done in 56 different ways.