A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of four hearts and one spade?

The answer is 9295

Step-by-step explanation:

Solution

A poker hands contains of = 5 cards

Ordinary deck of = 52 cards

Now we need to find the number of hands are there consisting of four hearts and one spade

Thus

The number of ways to get 4 hearts = ¹³C₄

=715

The number of ways to get to 1 spade = ¹³C₁

=13

Then

The total number of ways is given as:

715 * 13 = 9295

Therefore, the different hands that are available or present consisting of four hearts and one spade is 9295