# Choosing items from different types with restirctions.

• Sep 2nd 2011, 06:47 PM
bjnovak
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?
• Sep 2nd 2011, 06:55 PM
TKHunny
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?
• Sep 2nd 2011, 07:22 PM
bjnovak
Re: Probability question
would a be 5*4^19?
• Sep 3rd 2011, 03:19 AM
Plato
Re: Probability question
Quote:

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:
\$\displaystyle \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.