In how many ways can I package 6 colors of posterboard in packages of 5 posterboards each ?

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- Nov 16th 2009, 04:24 PMfholikCombinatorics Question
In how many ways can I package 6 colors of posterboard in packages of 5 posterboards each ?

- Nov 16th 2009, 06:32 PMSoroban
Hello, fholik!

Quote:

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.

- Nov 24th 2009, 11:34 AMfholikCombinatorics Question
I misstated the original problem. If you have an endless supply of posterboard in 6 different colors, in how many ways can you package 5 posterboards ?

- Nov 24th 2009, 11:48 AMPlato
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. - Nov 24th 2009, 12:46 PMfholikCombinatorics Question
That is the solution I was looking for. Thank you. fholik