3. For each of the following, indicate if it is a problem involving permutations, combinations, or neither, and then answer the question posed. Explain your reasoning.

a. How many groups of five songs can be chosen from a list of 35 songs?

b. How many ways can a person choose three different desserts from a dessert tray of eight desserts?

c. How many ways can a manager of a baseball team choose the lead-off batter and second batter from a baseball team of nine players?

d. How many ways are there to place seven distinct pieces of art in a row?

e. How many ways are there to randomly select four balls without replacement from a container of 15 balls numbered 1 to 15?

Step-by-step explanation:

a. How many groups of five songs can be chosen from a list of 35 songs?

Here combinations because order of songs selected doe snot matter hence

35C5 = 324632

b. How many ways can a person choose three different desserts from a dessert tray of eight desserts?

Here combinations

8C3 = 56

c. How many ways can a manager of a baseball team choose the lead-off batter and second batter from a baseball team of nine players?

Here order matters so 9P2 = 72

d. How many ways are there to place seven distinct pieces of art in a row?

Here we use permutations because distinct pieces so order matters.

7! ways

e. How many ways are there to randomly select four balls without replacement from a container of 15 balls numbered 1 to 15?

Without replacement we have to use combinations

15C4 = 1365