SOLUTION: Solve the problem. Five cards are drawn at random from an ordinary deck of 52 cards. In how many ways is it possible to draw all black cards? a. 32,890 b. 263,120 c. 65,78

Question 170425: Solve the problem.
Five cards are drawn at random from an ordinary deck of 52 cards. In how many ways is it possible to draw all black cards?
a. 32,890
b. 263,120
c. 65,780
d. 131,560
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
There are 26 black cards (13 spade and 13 club cards) to choose from. So this means that n=26. Since the amount per hand is 5 cards, this means that r=5

Since order does not matter, we must use the combination formula:

Start with the given formula

Plug in and

Subtract to get 21

Expand 26!

Expand 21!

Cancel

Simplify

Expand 5!

Multiply 26*25*24*23*22 to get 7,893,600

Multiply 5*4*3*2*1 to get 120

Now divide

So 26 choose 5 (where order doesn't matter) yields 65,780 unique combinations

So there are 65,780 possible ways to choose all black cards.

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