Notation and Theorem for Combinations

Notation

The number of all combinations of n objects, taken r at a time is denoted by C(n,r) or ⁿC_r.

ⁿC_r is defined when n and r are non-negative numbers.

Theorem

The number of all combinations of n distinct objects, taken r at a time is given by

ⁿC_r = n!/(n-r)!r!

Results from the theorem

ⁿC_r = [n(n-1)(n-2)...(n-r+1)]/(1.2.3...r)

ⁿC_n =1

ⁿC₀ = 1


ⁿC_r = ⁿP_r/r!