I know how to solve this problem using the Choose method, but I'm trying to do it this way and running into a problem. Could someone see where I'm going wrong?

Given a deck of 52 cards, what is the probability of drawing 1 ace, 1 two, 1 three, 1 four, and 1 five?

My answer:

(4/52) * (4/51) * (4/50) * (4/49) *(4/48)

because you have a 4 / 52 chance of drawing the ace, then a 4 / 51 chance of the two, and so on.

The question then goes on:

what is the probability of getting any straight?

I'm not able to figure this out, even using the Choose method.

My answer:

(8C1)(4C1)(4C1)(4C1)(4C1) / (52 C 5) = 0.000788

though the book's answer is 0.00355

The way I see this one is that you have (52 C 5) possibilities.

For the first card, anything works. For the second, there are eight possibilities. Then four for each subsequent card.

This strategy worked for the first half, but not here.