Question

1. herman has five different colored shirts: red, blue, yellow, purple, and gray. he will wear a different shirt each day this week from monday to friday. how many different ways can herman do this?

Explanation:

Step1: Determine choices for Monday

Herman has 5 shirt options for Monday.

Step2: Determine choices for Tuesday

Since one shirt is used, 4 options remain for Tuesday.

Step3: Determine choices for Wednesday

Two shirts are used, so 3 options left for Wednesday.

Step4: Determine choices for Thursday

Three shirts are used, so 2 options left for Thursday.

Step5: Determine choices for Friday

Four shirts are used, so 1 option left for Friday.

Step6: Calculate total permutations

Multiply the number of choices for each day: $5 \times 4 \times 3 \times 2 \times 1 = 5!$

Answer:

120