Answer:
2,808
Explanation:
To calculate the number of 5-card hands from a standard 52-card deck that contain three cards of one kind and two cards of another kind, you can use combinations.
First, choose the kind of cards you want to have three of. There are 13 kinds (one for each rank: 2 through Ace), so you have 13 choices for this.
Next, choose the kind of cards you want to have two of. Since you've already chosen one kind for three cards, you now have 12 choices left for the kind you want two of.
For each kind chosen, there are 4 cards of that kind in the deck (one in each suit).
Now, you need to calculate the number of ways to choose 3 cards out of the 4 of the first kind (three of a kind) and 2 cards out of the 4 of the second kind (two of a kind). You can calculate this using combinations:
Number of ways to choose 3 cards out of 4 for the first kind: C(4, 3) = 4 (since you want to choose 3 out of 4, and the order doesn't matter).
Number of ways to choose 2 cards out of 4 for the second kind: C(4, 2) = 6 (choose 2 out of 4).
Now, you can multiply the number of choices for each step together:
Number of 5-card hands with three of one kind and two of another kind = (Number of choices for the first kind) * (Number of choices for the second kind) * (Number of ways to choose 3 cards of the first kind) * (Number of ways to choose 2 cards of the second kind)
= 13 * 12 * 4 * 6
= 2,808
So, there are 2,808 different 5-card hands that contain three cards of one kind and two cards of another kind when dealt from a standard 52-card deck of playing cards.