If you are dealt 6 cards from a shuffled deck of 52 cards, find the probability of getting 3 jacks and 3 aces.
A) $\frac { 2 } { 2,544,815 }$
B) $\frac { 2 } { 13 }$
C) $\frac { 1 } { 1,017,926 }$
D) $\frac { 3 } { 26 }$

Question

If you are dealt 6 cards from a shuffled deck of 52 cards, find the probability of getting 3 jacks and 3 aces. 
A) $\frac { 2 } { 2,544,815 }$
B) $\frac { 2 } { 13 }$
C) $\frac { 1 } { 1,017,926 }$
D) $\frac { 3 } { 26 }$

Quizplus · Accepted Answer

The probability of getting 3 jacks and 3 aces from a 6-card hand can be calculated using combinations. There are 4 jacks and 4 aces in a deck of 52 cards. The number of ways to choose 3 jacks out of 4 is $\binom{4}{3}$, and the number of ways to choose 3 aces out of 4 is also $\binom{4}{3}$. The total number of ways to choose 6 cards out of 52 is $\binom{52}{6}$. Therefore, the probability is $\frac{\binom{4}{3} \times \binom{4}{3}}{\binom{52}{6}} = \frac{2}{2,544,815}$.

If You Are Dealt 6 Cards from a Shuffled Deck 22,544,815\frac { 2 } { 2,544,815 }2,544,8152​

If You Are Dealt 6 Cards from a Shuffled Deck $\frac { 2 } { 2,544,815 }$