# Combinatorics Question

• Nov 16th 2009, 04:24 PM
fholik
Combinatorics Question
In how many ways can I package 6 colors of posterboard in packages of 5 posterboards each ?
• Nov 16th 2009, 06:32 PM
Soroban
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 AM
fholik
Combinatorics 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 AM
Plato
Quote:

Originally Posted by fholik
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 ?

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 PM
fholik
Combinatorics Question
That is the solution I was looking for. Thank you. fholik