Fundamental Counting Principle

[raysfan30]

Take 4 pennies and 2 dimes. Now assume that you have no way to distinguish the
pennies from each other and no way to distinguish the dimes
from each other, but you can tell the difference between a dime
and a penny. For each of the following situations, how many
different ways can you pull coins from a bag. For instance, if I ask
for the number of ways for a bag with a penny and a dime, there
are 2 ways to pull the coins out of the bag: a penny followed by a
dime or a dime followed by a penny. Here are the situations: 4
pennies, 4 dimes, 2 pennies and 2 dimes, 3 pennies and 1 dime.
Finally, how many ways for 1 penny, 1 dime, 1 nickel and 1
quarter

 

[phonon44145]

C_n^k where n is number of pennies in the bag, k is number of pennies you want to take from the bag, gives you the number of ways to select the pennies. Similarly for the dimes. Then multiply the two results.