n inspector must select 4 tests to perform in a certain order on a manufactured part. He has a choice of 6 tests. How many ways can he perform 4 different tests?

Answer 1

This question is a bit ambiguous, "how many ways"?.

The number of combinations of n=six things taken r=four at a time is n!/r!(n-r)! = 6!/ (4!)(2!) = 6 x 5 / 2 = 15.

The r items can have r! different orders in which they are used, giving 4 x 3 x 2 x 1 = 24 permutations.

The number of different situations (ways?) becomes 15 x 24 = 360 when the selection options and the order options are considered.