a. The exclamation point is the symbol for "factorial". It means you form the product of the given integer and all smaller positive integers.
6! = 6×5×4×3×2×1 = 720
b. This notation is used to mean the number of permutations of 8 objects taken 5 at a time when order matters. In symbols, it means
nPk = n!/(n-k)!
In effect, you do the factorial thing as above, but you only include "k" factors in the product.
8P5 = 8×7×6×5×4 = 6720
c. Similar to nPk, the notation nCk means k objects chosen from n when order does not matter. Its formula is similar, but there's an extra division, so the number is smaller than nPk.
nCk = n!/(k!(n-k)!)
In effect, you only include k factors of the factorial, then you divide the result by k!.
12C4 = 12×11×10×9/(4×3×2×1) = 495
