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?

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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?

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Answer 1 · 2016-11-22T00:12:33

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 $26 \times 25 \times 26 \times 25 \times 24 = 10, 140, 000$ $26xx25xx26xx25xx24=10,140,000$

But since all orders are equal, we divide by the number of orders for a five card hand: $5 \times 4 \times 3 \times 2 \times 1 = 5! = 120$ $5xx4xx3xx2xx1=5! =120$ , so:

Answer: $\frac{10, 140, 000}{120} = 84, 500$ $(10,140,000)/120=84,500$

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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?

1 Answer

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