Two GRE Math Questions?

Hi and welcome to my blog,
I opened this blog to help anyone who is preparing for his GRE exam.
I remember myself when I started - I was so lost and in such a panic.
Luckily I got this great Gre guide that helped me a lot
So study hard and good luck!
Okay, I’m studying up for the GRE. My math is going nicely, but a few forms of discrete math are really fuzzy. The memory has gathered dust, y’see.
Anyhow, here’s one. Pretty simple I’m sure, but not much is stirring up in the old brain…:
There is a five question test. Of these five questions, only four need to be done. For the first two questions, there are three answer choices. For the last three questions, there are four answer choices.
The answer is 816, but upon fiddling around with the numbers some, I’m not quite following how they get to this answer. Makes me a tad bit upset that the site isn’t saying how they get these values, but at least they give ‘em.
Also, there’s another question, which is simple (I’m sure), but it’s not something I recall having done. The second question is as follows:
How many 5 digit numbers are there with distinct digits.
The answer is 27216
Pretty simple I’m sure, but I’ve run through a few Googles and not much is panning out.
Might make a few more questions across the next several weeks whenever I get stumped on something like this.
Okay, second question is solved. Much oblige. What about the first one, though?
There are total 10 digits.
The leftmost digit cannot be 0. Therefore leftmost digit has to be selected form the other 9 digits. Number of ways to select this digit = 9
1 digit has been selected from the 10 digits. The remaining 9 digits are to be used to fill the remaining 4 places. That can be done in 9C4 ways.
Total ways = 9 x 9C4 = 27216
i did GRE like a few yrs back, and scored a 410 in verbal, 800 in math, so yea gives me a 1210 out of 1600 which is just ok for graduate school. i suck at verbal i know.
but yea if you dont know how the 5 digits thing work, heres how
for a 5 digit number, you can’t have the first number to be 0, so yea, the first one has only 9 choices, give it a 9, the 2nd one has 10-1 choices,(with 0 ofcoz), so yea, another 9, the 3rd one has then only 8 choices, 4th one has 7, 5th one has 6, so yea 9times 9times 8 times 7 times 6 gives you umm yea the answer 27216