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?

Respuesta :

Answer:

The number of ways are 210.

Step-by-step 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 [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]

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

[tex]^{10}C_{4}=\frac{10!}{4!(10-4)!}[/tex]

[tex]^{10}C_{4}=\frac{10!}{4!6!}[/tex]

[tex]^{10}C_{4}=210[/tex]

Hence, the number of ways are 210.