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

Question

Quizplus · Accepted Answer

There are 12 picture cards in a deck (4 Jacks, 4 Queens, 4 Kings) and 40 non-picture cards. The probability of drawing 5 non-picture cards is the number of ways to choose 5 cards from the 40 non-picture cards divided by the number of ways to choose 5 cards from all 52 cards. This is calculated as $\frac{{\binom{40}{5}}}{{\binom{52}{5}}} = \frac{658,008}{2,598,960} = \frac{108,257}{108,290}$.

Compute Probabilities Involving Permutations and Combinations -If You Are Dealt 108,257108,290\frac { 108,257 } { 108,290 }108,290108,257​

Compute Probabilities Involving Permutations and Combinations
-If You Are Dealt $\frac { 108,257 } { 108,290 }$