SOLUTION: What is the probability of drawing a 5 card hand with the first 2 cards being hearts and the last 3 being spades in a standard deck of cards?

There are 13 hearts and 13 spades in a 52 card deck.

The 1st card will be a heart 13 times out of 52 or 13/52 or 1/4 of the time.

Now there is only a 51-card deck with only 12 hearts.
The 2nd card will be a heart 12 times out of 51 or 12/51 of those times.
That will happen (1/4)(12/51) = 1/17 of the time.

Now there is only a 50-card deck with all 13 spades.
The 3rd card will be a spade 13 times out of 50 or 13/50 of those times.
That will happen (1/4)(12/51)(13/50) = (1/17)(13/50) = 13/850 of the time.

Now there is only a 49-card deck with only 12 spades.
The 4th card will be a spade 12 times out of 49 or 12/49 of those times.
That will happen (1/4)(12/51)(13/50)(12/49) = (13/850)(12/49) = 78/20825
of the time.

Now there is only a 48-card deck with only 11 spades.
The 5th card will be a spade 11 times out of 48 or 11/48 of those times.
That will happen (1/4)(12/51)(13/50)(12/49)(11/48) = (78/20825)(11/48) =
143/166600 of the time.

Answer = 143/166600

Edwin