Hello everyone, Another example from the book i'm going over and i'm not exactly sure how they got their answer: The game of poker is played with an ordinary deck of cards. Various five-card holdings are given special names. a. how many 5 card poker hands contain two pair? Well i'm looking at the list, and I see two pair defined as this: Two cards of one denomination, two cards of a second denomination, and a 5th card of a thrid denomination. They said: consider forming a hand with two paris as a four-step process: Step 1: Choose the two denominations for the pairs. Step 2: Choose 2 cards from the small denomination Step 3: choose 2 card from the larger denomination Step 4: choose one card from the remianing. When they say denomination do they mean like: A,2,3,4,5,6,7,8,9,10,J,Q,K also why do they say choose 2 cards rfom the small and large denomination? couldn't u do it by getting like 2 kings, and 2 10's, and 1 other card like a 2? These are all large denominations. When i did this problem i thought it would be solved like this: You have 52 cards to pick from, but you only want 2 denominations, so Step 1: 52 choose 2 Step 2: You already used 2 cards so you only have 50 to choose from now, so 50 choose 2 Okay now you should have 4 cards, now you only need 1 more card, but you can't choose a card you picked in step 1 or 2, so u must take 52-4 = 48, 48 choose 2 (52 choose 2) * (50 choose 2) * (48 choose 1) But they did it the following way: total number of hands with two pairs: Step 1: 13 choose 2 Step 2: 4 choose 2 step 3: 4 choose 2 step 4: 44 choose 1 i'm not sure how they got this... Also the 44 choose 1, im not sure how they got 44. Any explanation would be great!