Question

g five cards are dealt from a standard deck of playing cards.what is the probability that the you dealt 5 cards from same suit.

Answer 1

the probability of being dealt 5 cards from the same suit is approximately 0.00198, or about 0.198%.

Explanation:

The total number of ways to choose 5 cards from a deck of 52 cards is given by the combination formula:

C(52, 5) = 52! / (5! (52 - 5)!) = 2,598,960

Now, we need to count the number of ways of choosing 5 cards from the same suit. There are 4 suits in a deck of cards (hearts, diamonds, clubs, and spades), so we need to count the number of ways to choose 5 cards from each of these suits and add them up.

For each suit, the number of ways of choosing 5 cards from that suit is given by the combination formula:

C(13, 5) = 13! / (5! (13 - 5)!) = 1,287

So the total number of ways of choosing 5 cards from the same suit is:

4 * 1,287 = 5,148

Therefore, the probability of getting 5 cards from the same suit is:

5,148 / 2,598,960 ≈ 0.00198

So the probability of being dealt 5 cards from the same suit is approximately 0.00198, or about 0.198%.