2. the director is also interested in the number of ways to choose a lead singer and a backup singer. in how many ways can the director choose a lead singer and then a backup singer?
indicate if this question involves a permutation or a combination. give a reason for your answer.

This question involves a Permutation as the order is important; the lead is chosen first, and then the backup singer is chosen.

Step-by-step explanation:

Consider the provided information.

Whenever the position or order matters, use permutation.

If position or order does not matter, then it's a case of combination.

Now director choose a lead singer and then a backup singer in this case position matters.

Suppose David is lead singer and John is backup singer this scenario is different form John is lead singer and David is backup singer.

Thus, order matter so we will use permutation.

47 - 90 = 43

43 - 180 = x

x = 137