Questions: Manufacturing Tests An inspector must select 5 tests to perform in a certain order on a manufactured part. He has a choice of 6 tests. How many ways can he perform 5 different tests? Use a graphing calculator. The number of ways the inspector can perform 5 different tests out of 6 tests is.

Solution Steps

To determine the number of ways the inspector can perform 5 different tests out of 6, we need to calculate the number of permutations of 5 tests chosen from 6. This is because the order in which the tests are performed matters. The formula for permutations is given by \( P(n, r) = \frac{n!}{(n-r)!} \), where \( n \) is the total number of items to choose from, and \( r \) is the number of items to choose.

To find the number of ways to perform 5 different tests out of 6, we use the permutation formula: \[ P(n, r) = \frac{n!}{(n-r)!} \] where \( n = 6 \) (total tests) and \( r = 5 \) (tests to perform).

Substituting the values into the formula, we have: \[ P(6, 5) = \frac{6!}{(6-5)!} = \frac{6!}{1!} \] Calculating \( 6! \): \[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \] Thus, we find: \[ P(6, 5) = \frac{720}{1} = 720 \]

Final Answer