Probability of a deck of cards

Question

You created a new deck of cards, using a standard deck of 52 plus a second set of spades (ace,2-10,jack,queen,king). From this new deck, 7 cards are picked at random. What is the probability that none of the 7 cards is a face card? Face cards are: jack, queen, king, and ace. Show all work.

Answer 1

Total number of 7 card "hands" is C(65,7) = N.

 

Number of hands without face cards is C(45,7) = N_A.

 

P(no face cards) = N_A/N.

 

 

 

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