Five cards are drawn...

Question

Five cards are drawn from a standard deck of 52 cards. How many hands of five cards have at least one black card?

Answer 1

Shelby,

            To calculate how many 5 card hands contain at least one black card it is easier to calculate how manny hands have no black cards and the subtract this from the total number of 5 card hands.

 

number of 5 card hands containing no black cards= ₂₆C₅=67,780

Total number of five card hands=₅₂C₅=2,598,960

Number of hands containing at least one black card=2,598,960-67,780=2,531,180.

 

We are using the principle that N(5 card hands)=N(5 card hands / no black cards)+N(5 card hands/at least one black card)

 

Hope this helps

 

Jim