In how many ways can I package 6 colors of posterboard in packages of 5 posterboards each ?
Hello, fholik!
In how many ways can I package 6 colors of posterboard in packages of 5 posterboards each?
Assuming that the order of the colors in a package does not matter,
. . we are choosing 5 colors from the available 6 colors.
There are: .$\displaystyle _6C_5 \:=\:{6\choose6} \:=\:6$ ways.
If the first answer is not what you meant, then I assume that a package could contain say three yellow, one green and one red.
If that is the case this is a multi-selection problem.
We can select $\displaystyle K$ items from $\displaystyle N$ different kinds in $\displaystyle \binom{K+N-1}{K}$ ways.