Question

eight cards are drawn from a standard deck of 52 cards. how many hands off with cards contain exactly three queens and three jacks g

Answer 1

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:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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

$C_{4,3}C_{4,3}C_{44,2} = \frac{4!}{1!3!} \times \frac{4!}{1!3!} \frac{44!}{2!42!} = 4*4*22*43 = 15136$

15,136 hands off with cards contain exactly three queens and three jacks.