What is the probability of getting 5 cards where 3 of them are kings, the 4th card is red and 5th is a black card?

Question

I know how to do the probability when I pick 3 card from the deck and all three are kings. But with this question, I am confused because I do not know if the 3 kings are two red and a black or 2 black and one red. So the number of red and black left in the deck after 3 kings are pick out are different (ie 24 reds left if 2 kings are red or 25 reds if 1 king is red).

Answer 1

"$3$ among $5$ are kings" and "the first three are kings" are quite different events.

You have four disjoint events to consider:

• A red non-king in 4th place, a black non-king in 5th place, then $3$ kings among the first three cards.
• A red king in 4th place, a black non-king in 5th place, then $2$ kings and $1$ non-king among the first three cards.
• A red non-king in 4th place, a black king in 5th place, then $2$ kings and $1$ non-king among the first three cards.
• A red king in 4th place, a black king in 5th place, then $1$ king and $2$ non-kings among the first three cards.