SOLUTION: You have a deck of 52 playing cards. What is the probability that a hand of 5 cards dealt randomly will contain 3 aces

Question 1058578: You have a deck of 52 playing cards. What is the probability that a hand of 5 cards dealt randomly will contain 3 aces
Answer by solve_for_x(190) (Show Source): You can put this solution on YOUR website!
There are 4 Aces in the deck, and 52 - 4 = 48 cards which are not Aces.

A five card hand that contains 3 Aces will contain 2 non-Aces.

The number of possible 5-card hands with 3 Aces is:

C(4, 3) * C(48, 2) = = 4 * 1128 = 4512 hands

The number of possible 5-card hands of any combination is:

C(52, 5) = = 2598960 hands

The probability of a hand with 3 Aces is then:

P(3 Aces) = 4512 / 2598960 = 94 / 54145 ≈ 0.001736
RELATED QUESTIONS
If you are dealt a 5 card hand from a standard deck of 52 playing cards, what is the... (answered by ewatrrr)

You are dealt two cards successively (with replacement) from a shuffled deck of 52... (answered by brysca)

You are dealt a hand of 4 cards from a standard deck of 52 playing cards. What is the... (answered by ewatrrr)

A 7 card hand is dealt from a standard deck of 52 playing cards. What is the probability (answered by ewatrrr)

In a standard deck of playing cards, there are 52 total cards. Half of the cards are red (answered by Edwin McCravy)

You are dealt 5 cards from a standard 52- card deck. What is the probability that your... (answered by stanbon)

What is the probability that I get at least 3 aces from a hand of 5 cards in a deck of 52 (answered by Edwin McCravy)

You are dealt 5 successive cards from a standard deck of playing cards. What is the... (answered by Edwin McCravy)

Suppose you are dealt six cards from a standard deck of 52 playing cards. What is the... (answered by ewatrrr)