If you are dealt 5 cards from a shuffled deck of 52 cards, find the probability that all 5 cards are picture cards.
A) $\frac { 33 } { 108,290 }$
B) $\frac { 3 } { 13 }$
C) $\frac { 1 } { 2,598,960 }$
D) $\frac { 1 } { 216,580 }$

Question

If you are dealt 5 cards from a shuffled deck of 52 cards, find the probability that all 5 cards are picture cards. 
A) $\frac { 33 } { 108,290 }$
B) $\frac { 3 } { 13 }$
C) $\frac { 1 } { 2,598,960 }$
D) $\frac { 1 } { 216,580 }$

Quizplus · Accepted Answer

The total number of picture cards in a deck is 12 (Jacks, Queens, Kings of each suit). The total number of ways to choose 5 cards out of 52 is $\binom{52}{5}$. The number of ways to choose 5 picture cards out of 12 is $\binom{12}{5}$. Therefore, the probability is $\frac{\binom{12}{5}}{\binom{52}{5}} = \frac{792}{2,598,960} = \frac{33}{108,290}$.

If You Are Dealt 5 Cards from a Shuffled Deck 33108,290\frac { 33 } { 108,290 }108,29033​

If You Are Dealt 5 Cards from a Shuffled Deck $\frac { 33 } { 108,290 }$