Euchre is a card game that uses a 24card deck which can be f

\"Euchre is a card game that uses a 24-card deck (which can be formed by removing all of the 2’s, 3’s, 4’s, 5’s, 6’s, 7’s, and 8’s from a standard 52-card deck) in which the players are each dealt 5-card hands from the deck of 24. Suppose that you are playing Euchre and are dealt a 5-card hand.\"

a) What is the probability that you are dealt no more than 2 tens?

b) What is the probability that you are dealt no queens and exactly 3 hearts?

Solution

a) Total cards = 24 x 52 = 1248

Cards removed = 24 x 4 x 7 = 672

Cards remaining (used in the game ) = 1248 - 672 = 576

the probability that you are dealt no more than 2 tens :

Case 1: zero 10\'s

Number of 10\'s = 24 x 4 = 96

Total cards left widout 10\'s = 576 - 96 = 480

Probability with zero 10\'s = 480C5

Case 2: 1 10\'s

Probability with one 10\'s =96C1 x 480C4

Case 2: 2 10\'s

Probability with two 10\'s =96C2 x 480C3

probability that you are dealt no more than 2 tens = 480C5 + 96C1 x 480C4 + 96C2 x 480C3

b) Total queens = 24 x 4 = 96

     Number of hearts = 24 x 6 = 144

     Cards without queens and hearts = 576 - 96 - 144 = 336

probability that you are dealt no queens and exactly 3 hearts = 144C3 x 336C2