Question

Of the 2,598,960 different five card hands from a 52 card deck, how many would contain 2 black cards and 3 red cards?

Answer 1

First we take the cards in order, and then we divide by the number of orders for the five cards, as order doesn't matter.

Explanation:

1st black card: 26 choices
2nd black card: 25 choices
1st red card: 26 choices
2nd red card: 25 choices
3rd red card: 24 choices

A total of `26xx25xx26xx25xx24=10,140,000`

But since all orders are equal, we divide by the number of orders for a five card hand: `5xx4xx3xx2xx1=5! =120`, so:

Answer: `(10,140,000)/120=84,500`