# Math Help - Combination

1. ## Combination

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

2. Hello, fholik!

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.

3. ## 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.

4. 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.
$\binom{4+9-1}{4}=495$

5. ## 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