Formulas

Combinations    CiK:    The number of combinations in K components taken i at a time.

CiK = K!/(i! (K-i)!)        for 0 <= i <= K

Example:    For i = 4 and K = 7

C47 = 7!/(4! (7-4)!) = 35

Factorial    F!:    The product of a set of n descending natural numbers.

F! = n * (n - 1) * (n - 2) * (n - 3) * . . . . * 1

By definition, 0! = 1

Example:    For n = 6

6! = 6 * 5 * 4 * 3 * 2 * 1 = 720

Permutations    PiK:    The number of ordered combinations in K components taken i at a time.

PiK = K!/(K-i)!        for 0 <= i <= K

Example:    For i = 4 and K = 7

P47 = 7!/(7-4)! = 840

Product    Π ni = 0 xi :    The mathematical multiplication of a set of numbers.

P = Π ni = 0 xi = x0 * x1 * x2 * x3 * . . . . * xn

Example:    For x0 = 17, x1 = 28, x2 = 156, x3 = -5, and x4 = 17

P = Π 4i = 0 xi = 17 * 28 * 156 * -5 * 17 = -1262347

Summation    Σ ni = 0 xi :    The mathematical sum of a set of numbers.

S = Σ ni = 0 xi = x0 + x1 + x2 + x3 + . . . . + xn

Example:    For x0 = 17, x1 = 28, x2 = 156, x3 = -5, and x4 = 17,

S = Σ 4i = 0 xi = 17 + 28 + 156 + -5 + 17 = 213

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