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?

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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):
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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