# Math Help - How many ways

1. ## How many ways

How many ways can first and second awards and three honorable mention awards be given to nine contestants?
This one is hard but I came up with 6,048 awards given away. is this right. Thanks for any help given.

2. Hello, kwtolley!

This one is similar to the committee-selection problem.

How many ways can first and second awards and three honorable mention awards
be given to nine contestants?

I came up with 6,048. is this right? . Sorry, no

The first award can be given to any of the $9$ contestants.
The second award can be given to any of the $8$ other contestants.
The honorable mentions are given to three of the other seven contestants
. . in $C(7,3) \,= \,\frac{7!}{3!4!}\,=\,35$ ways.

Therefore: . $9 \times 8 \times 35\:=\:2520$ ways.