Solve the problem.
-Five cards are drawn at random from an ordinary deck of 52 cards. In how many ways is it possible to draw two red cards and three black cards?
A) 422,500 ways
B) $1,690,000$ ways
C) 845,000 ways
D) $1,267,500$ ways

Question

Quizplus · Accepted Answer

To solve this, we use combinations. There are 26 red cards and 26 black cards in a deck. We need to choose 2 red cards from 26 and 3 black cards from 26. The number of ways to choose 2 red cards is $ \binom{26}{2} $ and the number of ways to choose 3 black cards is $ \binom{26}{3} $. The total number of ways is the product of these two combinations: $ \binom{26}{2} \times \binom{26}{3} = 325 \times 260 = 845,000 $.

Solve the Problem 1,690,0001,690,0001,690,000 Ways C) 845,000 Ways D) 1,267,5001,267,5001,267,500 Ways

Solve the Problem $1,690,000$ Ways
C) 845,000 Ways
D) $1,267,500$ Ways