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

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- Mar 31st 2010, 08:58 AMfholikCombination
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 AMSoroban
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: .$\displaystyle 9^4 \,=\,6561$ ways.

- Mar 31st 2010, 12:57 PMfholikcombination
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 PMPlato
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 $\displaystyle \binom{K+N-1}{K}$.

Here the choices are identical and the pizzas are different.

$\displaystyle \binom{4+9-1}{4}=495$ - Apr 1st 2010, 04:18 AMfholikcombination
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