SOLUTION: 5 Cards are drawn randomly from a regular deck of cards. How many ways can you draw 5 cards and get 4 hearts and 1 spade?

Question 1191200: 5 Cards are drawn randomly from a regular deck of cards. How many ways can you draw 5 cards and get 4 hearts and 1 spade?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

We'll use the nCr combination formula because order doesn't matter when selecting the cards.

Let's find out how many ways there are to select the four hearts
n = 13 hearts total
r = 4 to select

n C r = (n!)/(r!(n-r)!)
13 C 4 = (13!)/(4!*(13-4)!)
13 C 4 = (13!)/(4!*9!)
13 C 4 = (13*12*11*10*9!)/(4!*9!)
13 C 4 = (13*12*11*10)/(4!)
13 C 4 = (13*12*11*10)/(4*3*2*1)
13 C 4 = (17160)/(24)
13 C 4 = 715

There are 715 ways to pick the four hearts.

Then there are 13C1 = 13 ways to pick the 1 spade since we have 13 spades to pick from and one slot to fill.

The number of five card hands with four hearts and one spade is therefore: 715*13 = 9295

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