There are 5 sheets of distinct A stamps and 5 sheets of distinct B stamps for a total of 10 sheets of distinct stamps. The album is put together using a combination of three sheets of A or B stamps and two sheets of the other for a total of 5 sheets. How many combinations of the album would there be if you used all 10 sheets of the A & B stamps with the three / two sheet split.
Any help would be greatly appreciated!
I assume you mean you choose either three A's and two B's or two A's and three B's. Hint: For the first, there are ${5 \choose 3}=10$ ways to select the A's. How many ways for each of these to select the B's? Because of the "for each" you multiply them. Then count up the two A's/three B's cases the same way.
First of all, you have two choices for the three sheet split: either A or B. Then you have to choose 3 sheets from what you choose.
$${2\choose1}\cdot{5\choose 3} = 2\cdot10 = 20$$
Now for the "two sheet split", we have one choice of where the cards have to be from(that is A or B) .Then we have to choose 2 from 5.
$$1\cdot{5\choose2}=10$$
Since we have to both of the tasks, we multiply to get $20*10=\boxed{200}$
