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

1) 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 1 queen?

b) What is the probability that you are dealt no aces and exactly 2 hearts?

2)A 7-character password consists of three numbers (from 2 to 9) followed by four letters (from A to N).

a) How many different passwords can be formed that have no repeated number or letters?

b) How many different passwords can be formed if letters and numbers can be repeated?

Solution

1)

a) There are total 4 queens and 20 other cards.

Hence , Probability = 4/24 * (20/23 * 19/22 * 18/21 * 17/20) = 0.091 Answer

b) Probability = (5/24 * 4/23) * (15/22 * 14/21 * 13/20) = 0.011 Answer

2)

a) Number of different passwords = (8*7*6) * ( 14 * 13 * 12 * 11) = 8072064 Answer

b) Number of different passwords = ( 8*8*8) * (14*14*14*14) = 19668992 Answer