Question

Deck of 52 cards: You draw 5 cards.

How many possible combinations are possible containing: 3 of a kind, ` pair of a different value

Answer 1

1 pair of a different value

Answer 2

lets do three kings, 2 aces

Answer 3

there are 4 kings, so \(\binom{4}{3}=4\)ways to get 3 of them
then there are 4 aces so \(\binom{4}{2}=6\) ways to choose 2 of them
all together \(4\times 6=24\) ways to get 3 kings, two aces

Answer 4

all that is left is to figure out how many ways to pick two different face values

Answer 5

how would you do the two different values

Answer 6

12 C 2?

Answer 7

@reemii

Answer 8

A typical result: {XXX, YY}, where
- X is any value from 1,2,...,10,J,Q,K
- Y is any value from 1,2,...,10,J,Q,K, but without X which is already chosen.
It's a "cumulative" way of counting. Make steps, at each step, count the "number of ways to choose ...", then multiply the numbers.

Sometimes, different orders are possible. For example
(A)
(1) Choose value X, -> how many ways = \(n_1\)
(2) select 3 'X' from the 4 'X' in the deck -> how many ways = \(n_2\)
(3) choose value Y -> how many ways = \(n_3\)
(4) choose 2 'Y' in the deck -> how many ways = \(n_4\)
(5) answer is \(n_1\times n_2 \times n_3 \times n_4\)
(B)
(1) Choose 'X' and 'Y' -> ...
(2) choose which one is the pair -> ...
(3) choose the cards to make a pair ->
(4) choose the cards for the three of a kind -> ...
(5) compute the product.
You might come up with other steps.

Can you try (A) for example?
(A1) choose X -> 13 ways
(A2) choose 3 cards from value X -> \(\binom43\)
(A3) choose Y -> 12 ways
(A4) etc.

Answer 9

wow this is a lot to take in

Answer 10

It's ok I understand this one thatnks