SOLUTION: Three cards are selected at random from a standard deck of 52 playing cards. Determine the probability that all three cards are: a) Hearts b) Black c) Aces d) Face cards

Algebra ->  Probability-and-statistics -> SOLUTION: Three cards are selected at random from a standard deck of 52 playing cards. Determine the probability that all three cards are: a) Hearts b) Black c) Aces d) Face cards      Log On


   

Question 1117677: Three cards are selected at random from a standard deck of 52 playing
cards. Determine the probability that all three cards are:
a)
Hearts
b)
Black
c)
Aces
d)
Face cards
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Three cards are selected at random from a standard deck of 52 playing
cards. Determine the probability that all three cards are: 
(The denominator of all the probabilities will be 
52 cards choose 3 = 52C3 = 22100)

a)
Hearts
number of ways to select 3 hearts =

13 hearts choose 3 = 13C3 = 286

Probability = 286/22100 = 11/850

b)
Black
number of ways to select 3 black cards:

26 black cards choose 3 = 26C3 = 2600

Probability = 2600/22100 = 2/17

c)
Aces
number of ways to select 3 aces:

4 aces choose 3 = 4C3 = 4 ways

Probability = 4/22100 = 1/5525

d)
Face cards
number of ways to select 3 face cards:

12 face cards choose 3 = 12C3 = 220

Probability = 220/22100 = 11/1105

Edwin