Please help with Part A and B Thanks Euchre is a card game t

Please help with Part A and B. Thanks!

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 spade?

b) What is the probability that you are dealt no diamonds and exactly 2 jacks?

Solution

Total cards = 24

five cards can be drawsn in 24C5 ways = 24!/(5!*19!)=42504;

Probability that no more than one spade = Probability of no spade + Probability of one spade

total 6 spades. No spade means, all five cards should be selected from 24-6 = 18 cards

five cards can be selected from 18 cards in 18C5ways= 8568

Probability of no spade = 8568/42504 = 0.201581

selecting one spade, one spade from 6 spades and remaining 4 cards from selected 24-6 =18 cards

number of ways of selecting one spade = (6C1) * (18C4) =4*4845 = 18360

Probability of one spade = 19380/42504 = 0.431959

Probability that no more than one spade = 0.63354

No diamonds and exactly two jacks can be selected as

removing 6 diamonds , number of cards = 24-6 =18

in the 18 cards there are four jacks, from 4 jacks , two can be selected in 4C2 ways = 6

number of ways to select the remaining three cards from 14 (18-4 jacks) is 14C3 ways= 364

number of ways no diamonds and exactly 2 jacks = 6*364 = 2184

probability that you are dealt no diamonds and exactly 2 jacks=2184/42504 =0.051383