Question

9. Brett has ten distinct T-shirts. He is planning on going on a short weekend trip to visit his brother in college. He has enough room in his bag to pack four T-shirts. How many different ways can he choose four T-shirts for his trip?

Answer 1

The number of ways are 210.

Explanation:

Consider the provided information.

Brett has ten distinct T-shirts. He is planning on going on a short weekend trip to visit his brother in college. He has enough room in his bag to pack four T-shirts.

Since order doesn't matter so we will use combination.

Use the formula for combination
`^(n)C_(r)=(n!)/(r!(n-r)!)`

Substitute n=10 and r=4 in above formula.

`^(10)C_(4)=(10!)/(4!(10-4)!)`

`^(10)C_(4)=(10!)/(4!6!)`

`^(10)C_(4)=210`

Hence, the number of ways are 210.