If you are dealt 5 cards from a shuffled deck of 52 cards, find the probability that none of the 5 cards are picturecards.
A) $\frac { 108,257 } { 108,290 }$
B) $\frac { 3 } { 13 }$
C) $\frac { 33 } { 108,290 }$
D) $\frac { 1 } { 216,580 }$

Question

If you are dealt 5 cards from a shuffled deck of 52 cards, find the probability that none of the 5 cards are picturecards. 
A) $\frac { 108,257 } { 108,290 }$
B) $\frac { 3 } { 13 }$
C) $\frac { 33 } { 108,290 }$
D) $\frac { 1 } { 216,580 }$

Quizplus · Accepted Answer

There are 12 picture cards in a deck (Jacks, Queens, Kings of each suit), leaving 40 non-picture cards. The probability of drawing 5 non-picture cards is the combination of choosing 5 from 40 divided by the combination of choosing 5 from 52, which is $\frac{{40 \choose 5}}{{52 \choose 5}} = \frac { 108,257 } { 108,290 }$.

If You Are Dealt 5 Cards from a Shuffled Deck 108,257108,290\frac { 108,257 } { 108,290 }108,290108,257​

If You Are Dealt 5 Cards from a Shuffled Deck $\frac { 108,257 } { 108,290 }$