There are 12 different-colored crayons in a box. How many ways can Karl select four crayons if the order in which he draws them out does not matter?
I need to count the number of combinations of four crayons out of 12, without regard to order. I recall that the formula for the number of combinations of n objects taken r at a time is nCr = n! / (r! (n-r)!), where n! is the factorial of n, meaning the product of all positive integers up to n. In this case, n = 12 and r = 4, so I plug those values into the formula and simplify. 12C4 = 12! / (4! (12-4)!) = (12 x 11 x 10 x 9 x 8!) / (4 x 3 x 2 x 1 x 8!) = (12 x 11 x 10 x 9) / (4 x 3 x 2 x 1) = 495. Therefore, there are 495 ways for Karl to select four crayons out of 12. 