This exercise refers to a standard deck of playing cards. assume that 5 cards are randomly chosen from the deck. how many hands contain exactly two 3s and two 7s?

Total number of cards in hand contain exactly two 3s and two 7s is 56.

Step-by-step explanation:

Given : This exercise refers to a standard deck of playing cards. Assume that 5 cards are randomly chosen from the deck.

To find : How many hands contain exactly two 3s and two 7s?

Solution :

In a standard deck of card has 52 cards distributed in 4 sets.

Each set has {2,3,4,5,6,7,8,9,10,J,Q,K,A} has 13 cards.

Number of 3s in 52 cards are 4.

Number of 7s in 52 cards are 4.

So, Getting exactly two 3s out of 4 is

Getting exactly two 7s out of 4 is

The fifth card is from remaining cards i.e. 52-8=44

Getting fifth card is

Total number of cards in hand contain exactly two 3s and two 7s is

Therefore, Total number of cards in hand contain exactly two 3s and two 7s is 56.