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.

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- Jul 9th 2006, 01:40 AMkwtolleyHow 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. - Jul 9th 2006, 03:50 AMSoroban
Hello, kwtolley!

This one is similar to the committee-selection problem.

Quote:

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 $\displaystyle 9$ contestants.

The second award can be given to any of the $\displaystyle 8$ other contestants.

The honorable mentions are given to three of the other seven contestants

. . in $\displaystyle C(7,3) \,= \,\frac{7!}{3!4!}\,=\,35$ ways.

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

- Jul 10th 2006, 08:05 AMkwtolleyThanks
you for checking my answer