Solve the problem.
-Suppose 6 cards are drawn from a deck of 52 cards. What is the probability of drawing 4 spades and 2 hearts?
A) $\frac { 429 } { 156,604 }$
B) $\frac { 1 } { 783,020 }$
C) $\frac { 143 } { 6664 }$
D) $\frac { 144 } { 72,709 }$

Question

Solve the problem.
-Suppose 6 cards are drawn from a deck of 52 cards. What is the probability of drawing 4 spades and 2 hearts? 
A) $\frac { 429 } { 156,604 }$
B) $\frac { 1 } { 783,020 }$
C) $\frac { 143 } { 6664 }$
D) $\frac { 144 } { 72,709 }$

Quizplus · Accepted Answer

The probability of drawing 4 spades and 2 hearts from a deck of 52 cards can be calculated using combinations. There are 13 spades and 13 hearts in a 52-card deck. The number of ways to choose 4 spades out of 13 is $ \binom{13}{4} $, and the number of ways to choose 2 hearts out of 13 is $ \binom{13}{2} $. The total number of ways to draw 6 cards out of 52 is $ \binom{52}{6} $. Therefore, the probability is $ \frac{\binom{13}{4} \cdot \binom{13}{2}}{\binom{52}{6}} $, which simplifies to $ \frac { 429 } { 156,604 } $.

Solve the Problem 429156,604\frac { 429 } { 156,604 }156,604429​ B) 1783,020\frac { 1 } { 783,020 }783,0201​

Solve the Problem $\frac { 429 } { 156,604 }$ B) $\frac { 1 } { 783,020 }$