An old question. How many different hands can you draw with one pair?
I have read an answer and explanation from another post which i understand. What i don't understand is where i fail in my own logic.
For the first card, you can draw one of 52 cards. For the second, you can draw one of 3 cards in order to make a pair. The third card can be any of 48 cards to avoid 3 of a kind. Fourth card can be any of 44 cards to avoid 3 of a kind and two pair. Last card can be any of 40 cards to avoid 3 of a kind and two pair.
The answer should then be $52*3*48*44*40=13178880$ , but this is much larger than the actual answer.