Answer:
15,136 hands off with cards contain exactly three queens and three jacks.
Step-by-step explanation:
The order in which the cards are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Standard deck:
4 queens and 4 jacks.
The other 52 - 8 = 44 cards are neither queens nor jacks.
Wow many hands off with cards contain exactly three queens and three jacks?
3 queens from a set of 4.
3 jacks from a set of 4.
2 other cards(not queens neither jacks) from the other 44. So
[tex]C_{4,3}C_{4,3}C_{44,2} = \frac{4!}{1!3!} \times \frac{4!}{1!3!} \frac{44!}{2!42!} = 4*4*22*43 = 15136[/tex]
15,136 hands off with cards contain exactly three queens and three jacks.
