In playing poker, the likelihood of being dealt a particular hand depends on the number of ways in which that hand could have been dealt from the 52-card deck. Find the number of ways each hand could be dealt.

Two pairs (one pair each of two different face values and a card of a third face value)

To find the number of ways a two pairs hand can be dealt in poker, we need to consider the following:

1. Choose the two face values for the pairs: Since there are 13 possible face values in a deck of cards, we can choose any two of them, giving us C(13, 2) combinations.

2. Choose the two suits for the first pair: Within each face value pair, there are four suits, and we need to choose two of them. This can be done in C(4, 2) ways.

3. Choose the two suits for the second pair: For the remaining face value pair, we again need to choose two out of the available four suits, which again can be done in C(4, 2) ways.

4. Choose the remaining card: Once the two pairs are determined, we have to choose any card from the remaining 44 cards (52 cards - 4 cards for the two pairs - 2 cards for the third face value pair).

To find the total number of ways, we need to multiply the results from steps 1 to 4:

Total number of ways = C(13, 2) * C(4, 2) * C(4, 2) * 44

Evaluating this expression will give us the total number of ways a two pairs hand can be dealt from a standard 52-card deck in poker.