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.
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 $\displaystyle 9$ 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.