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

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

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) = (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) = (4!)/(1!3!) * (4!)/(1!3!) (44!)/(2!42!) = 4*4*22*43 = 15136`

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