# There's a deck of 52 cards. A five-card hand has three of a kind consists of 3 cards of the same rank, one card of another, and one card of another. How many different 3-of-a-kind hands are there?

To get a three-of-a-kind, we have 3 of one ordinal, and 2 other cards that are not the same ordinal as the first three or each other.

In all of the calculation, we're using combinations (we don't care about the order of the card draw):

There are 13 ordinals in a deck of cards (Ace, or 1, through 10, and then Jack, Queen, and King). We are picking one of the ordinals:

and from that ordinal we want 3 of the suits (there are 4 suits for each ordinal - Spades, Hearts, Clubs, Diamonds):

We then need to get 2 more cards. They can't be of the same ordinal as the first one or each other (so that's 12 remaining ordinals and we're picking 2). We want one of each:

and now we can calculate this:

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- When a event is reported, the probability that is a negative event is 30%. What is the probability that 3 out of 5 reported events are negative?
- A lottery has a $100 000 first prize, a $25 000 second prize, and five $500 third prizes. A total of 50000 tickets are sold. What is the probability of winning a prize in this lottery?
- How do you evaluate 6p4?
- How many permutations are there of the letter in the word baseball?
- The camera club has five members, and the mathematics club has eight. There is only one member common to both clubs. In how many ways could a committee of four people be formed with at least one member from each club?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7