And show your work for all three. you so much. evaluate.. a. 6! b. 8p5 c. 12c4

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