# Combination

• Mar 31st 2010, 08:58 AM
fholik
Combination
If I have 9 varieties of pizza to choose from, in how many ways can I choose 4 slices of pizza ?
• Mar 31st 2010, 09:26 AM
Soroban
Hello, fholik!

Quote:

If I have 9 varieties of pizza to choose from,
in how many ways can I choose 4 slices of pizza?

For each of the four slices, you have 9 choices of variety.

Therefore, there are: . $9^4 \,=\,6561$ ways.

• Mar 31st 2010, 12:57 PM
fholik
combination
Thanks for the reply, but your method leaves duplicate choices. This question came from an state-sponsored math exam and the correct response is 495. I just need to find the formula for future reference.
• Mar 31st 2010, 01:38 PM
Plato
Quote:

Originally Posted by fholik
Thanks for the reply, but your method leaves duplicate choices. This question came from an state-sponsored math exam and the correct response is 495. I just need to find the formula for future reference.

The question is vague. But the given answer implies a multi-set.
The number of ways to put K identical units into N different cells is $\binom{K+N-1}{K}$.
Here the choices are identical and the pizzas are different.
$\binom{4+9-1}{4}=495$
• Apr 1st 2010, 04:18 AM
fholik
combination
Thank You, Plato. That is the formula I was looking for. I had seen it a few months ago, but had forgotten. Thanks for reminding me. I will write it down this time. Fholik