Respuesta :
Answer:
108288 poker hands contain two or three queens.
Step-by-step explanation:
Consider the provided information.
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.
We need to find How many poker hands contain two or three queens?
Case I: Two queens
[tex]\binom{48}{3}\binom{4}{2}=\frac{48!}{3!45!}\cdot\frac{4!}{2!2!}[/tex]
Case II: Thee queens
[tex]\binom{48}{2}\binom{4}{3}=\frac{48!}{2!46!}\cdot\frac{4!}{3!1!}[/tex]
Thus, the total number of ways:
[tex]\frac{48!}{3!45!}\cdot\frac{4!}{2!2!}+\frac{48!}{2!46!}\cdot\frac{4!}{3!1!}=108288[/tex]
Hence, 108288 poker hands contain two or three queens.
