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

Algebra ->  Probability-and-statistics -> 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      Log On


   

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) About Me  (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:


n%21%2F%28n-r%29%21r%21 Start with the given formula



26%21%2F%2826-5%29%215%21 Plug in n=26 and r=5



26%21%2F21%215%21 Subtract 26-5 to get 21


Expand 26!



Expand 21!




Cancel



%2826%2A25%2A24%2A23%2A22%29%2F5%21 Simplify


Expand 5!
%2826%2A25%2A24%2A23%2A22%29%2F%285%2A4%2A3%2A2%2A1%29



7893600%2F%285%2A4%2A3%2A2%2A1%29 Multiply 26*25*24*23*22 to get 7,893,600



7893600%2F120 Multiply 5*4*3*2*1 to get 120



65780 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.