# Thread: Choosing items from different types with restirctions.

1. ## Choosing items from different types with restirctions.

A store sells 5 different types of office supplies: pencils, mechanical pencils, pens, erasers, and highlighters. How many ways are there to choose:

a) 20 supplies?

b) 20 supplies with at least one of each office supply?

c) 20 supplies with at least 4 erasers and 2 pens?

2. ## Re: Probability question

Think hard. You probably have the tools.

I like part B. Can you reduce the problem by simply picking one of each of the supplies and then worrying about how to choose 15 with no additional restriction?

3. ## Re: Probability question

would a be 5*4^19?

4. ## Re: Probability question

Originally Posted by bjnovak
would a be 5*4^19?
No, not even close.
The number of ways to put N identical objects into K different cells is:
$\binom{N+K-1}{N}~.$

In your problem part a) the choices are identical, N=20.
The supplies are different, K=5.

For b) use reply #2 so N=15.