Question

How many ways are there to choose eight coins from a piggy bank containing 100 identical pennies and 80 identical nickels

Answer 1

8P give 1 way.
8N give 1 way.
1P 7N give:
\[\frac{8!}{7!}=8\ ways.\]
2P 6N give:
\[\frac{8!}{2!6!}=28\ ways.\]
3P 5N give:
\[\frac{8!}{3!5!}=56\ ways.\]
4P 4N give:
\[\frac{8!}{4!4!}=70\ ways.\]
5P 3N give 56 ways.
6P 2N give 28 ways.
7P 1N give 8 ways.
The total number of of ways to choose eight coins is give by:
1 + 1 + 8 +28 +56 + 70 + 56 +28 + 8 = you can calculate.