Question

A standard deck of cards contains 52 cards. The cards have 4 different suits: clubs, diamonds, hearts, and spades. For each suit, there are 13 cards: one for each of the values 2 through 10, jack (J), queen (Q), king (K), and ace (A). A poker hand consists of 5 cards chosen at random from a standard deck.a. How many poker hands have two or more aces? b. How many poker hands contain the king of diamonds, the queen of hearts, or both?

Answer 1

Answer:

108336,42875

Step-by-step explanation:

given that a standard deck of cards contains 52 cards. The cards have 4 different suits: clubs, diamonds, hearts, and spades. For each suit, there are 13 cards: one for each of the values 2 through 10, jack (J), queen (Q), king (K), and ace (A).

no of cards in poker = 5

a) For having 2 or more aces, we have

(2 aces, 3 non aces) or (3 aces, 2 non aces) or (4 aces, 1 non ace)

No of ways = $4C2*48C3 +4C3*48C2+4C4*48C1\\=108336$

b) For having King diamonds, or queen of hearts, or both,

we can have either

(K dice and any four of cards from other 51) Or (q hearts and any four of cards from other 51) - (k dice, q hearts and 3 cards from other 50)

= $51C3+51C3-50C2 \\=41650+1225\\=42875$