- #1

alexmahone

- 304

- 0

**My attempt:**

Let us first pick the 3 different ranks. There are \(\displaystyle {13\choose 3}\) ways of doing this.

Out of each rank consisting of 4 suits, we must pick 2 cards, 2 cards and 1 card respectively.

So, no. of ways \(\displaystyle ={13\choose 3}\cdot {4\choose 2}\cdot {4\choose 2}\cdot {4\choose 1}\)

Total no. of ways of selecting a five-card poker hand \(\displaystyle ={52\choose 5}\)

\(\displaystyle p=\dfrac{{13\choose 3}\cdot {4\choose 2}\cdot {4\choose 2}\cdot {4\choose 1}}{{52\choose 5}}\)

This doesn't match the answer given in the textbook. Where have I gone wrong?