I just can't seem to get this problem, and time is running out.

The problems on this page all deal with hands taken from a deck of 32 cards:

the 7, 8, ... , Q, K, A of each of the four suits.

How many five-card hands are possible which satisfy:

the hand has exactly two hearts

the hand has exactly two spades

the hand has exactly two Kings

For this problem I set up the three cases like this: (O = non-heart, non-spade suits)

1KH - 7H - 1KS - 7S - 14O

1KH - 7H - 7S - 6S - 1KO

7H - 6H - 1KS - 7S - 1KO

Then I multiplied and added them together and got the

correct answer of 1274.

However, I can't seem to figure out the second and third

problems.

How many 6-card hands are possible which satisfy:

the hand has exactly two hearts

the hand has exactly three spades

the hand has exactly 2 Kings

I tried setting up the cases the same as in problem #1, with

the necessary modifications:

1KH - 7H - 1KS - 7S - 6S - 14O

1KH - 7H - 7S - 6S - 5S - 1KO

7H - 6H - 1KS - 7S - 6S - 1KO

But My answer of 7350 is wrong and I can't figure out what

I'm doing wrong.

Similarly, I can't figure out the 3rd problem:

How many 6-card hands are possible which satisfy:

the hand has exactly two hearts

the hand has exactly three spades

I would think it would simply be:

8H - 7H - 8S - 7S - 6S - 16O multiplied together, but it isn't.

Any Help would be great.