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## Homework Statement

In five-card poker, a straight consists of five cards with adja-cent denominations (e.g., 9 of clubs, 10 of hearts, jack of hearts, queen of spades, and king of clubs). Assuming that

aces can be high or low, if you are dealt a five-card hand, what is the probability that it will be a straight with high card 10? What is the probability that it will be a straight?

What is the probability that it will be a straight flush (all cards in the same suit)?

## Homework Equations

## The Attempt at a Solution

First, I calculated the number of possible 5-card hands that can be dealt out: [itex]{{52}\choose{5}}=2598960[/itex]. To answer the first question, I imagined how the cards could be dealt out to generate a straight, since order doesn't matter. I know that, to make a straight, Jacks , Queens, Kings, Aces, 1s, 2s ,3s 4s, and 5s are out of the question. So, if I was dealt a 10, there would be 4 choices (two black and two red); and since either a red or a black will be chosen, then there are only two possibilities for the 9. If the 10 happened to be hearts or diamonds, then the the 9 would have to be a spades or clubs. Using this reasoning for the rest of them, I calculated that there would [itex]4 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 64 [/itex] different straight hands with 10 as the highest card. Thus, the probability would be [itex]\frac{64}{2598960}=.000024625[/itex]. However, the answer is .000394. What did I do wrong?