n the game of euchre the deck consists of the 9 10 jack quee

n the game of euchre, the deck consists of the 9, 10, jack, queen, king and ace of each suit. Players are dealt a five card hand. What is the probability that a player is dealt 2 hearts

Solution

Euchre uses a pack of 24 cards, consisting of ace, king, queen, jack, 10, and 9 in each of the four suits.

In Euchre, a hand consists of 5 cards.

We fin the probability that a hand includes four hearts.

The number of ways getting 4 hearts from 6 hearts is 6c₄ = 15 and remaining one card is drawn from none of heart cards, the possible ways 18c₁ = 18.

The favourable cases = 15*18 = 270.

The exhaustive case, the number of possibles of getting 5 cards from 24 cards, is 24c₅ =42504

The required probability is 270 / 42504 = 0.00635