I had to solve for this:

1) choose 4 people from a class of 12
My answer:
n=12 r=4
12C4 = 495

2) chosse 8 people from a class of 12
my answer:
n=12
r=8
12C8 = 495

why is it that they both eqaul 495? maybe I am doing it wrong but I am confused why do they both equal 495?

They are the same, both 2 from the mean of 6. If you do 12C6, you get the max. A neat thing to do is to graph each possibilty,
12C1
12C2
12C3 and so on until

12C12.

Graph number combinations vs n.

If you smooth it up, you get the binomial approximation to the normal probability curve.

thanks bobpursley

to go along with what bobpursley showed you, try to finish this pattern

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
...
.
.
to get a new number, add the one immediately above and one to the left, the left column is made up of 1's

This is Pascal's Triangle. Look at the row that starts with 1 12 ...
Did you notice something?

Yes, you are correct that both 12C4 and 12C8 equal 495. This may seem surprising, but it actually follows a pattern in combinatorics called Pascal's Triangle.

Pascal's Triangle is a triangular pattern of numbers, where each number is the sum of the two numbers directly above it. It starts with a 1 at the top, and each row begins and ends with a 1. The rows in Pascal's Triangle represent the coefficients in the expansion of the binomial (a + b)^n.

If you look at the 12th row of Pascal's Triangle, you will see that it starts with 1, followed by the numbers 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, and ends with 1. These numbers are the coefficients of the binomial expansion of (a + b)^12.

Now, in your case, the values of 12C4 and 12C8 are the 5th and 9th numbers in the 12th row of Pascal's Triangle. Since Pascal's Triangle is symmetric, the 5th and 9th numbers are the same, and that is why both 12C4 and 12C8 equal 495.

This symmetry in Pascal's Triangle occurs because choosing "k" items from a set of "n" is the same as choosing "n-k" items from the same set. In other words, 12C4 is equal to 12C8. This property of symmetry is why you are observing the same value for both combinations.