^{R}(n,r) = C(n+r-1,r) = (n+r-1)!/r!(n – 1)!, where both n and r should be >= 0.

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## Combinations with replacement formula

The combinations with replacement are by convention denoted by C^{R}(n,r):

Initial notation: C^{R}(n,r) = C(n + r - 1,r)

Intermediary form: C^{R}(n,r) = (n + r - 1)! / r! (n + r - 1 - r)!

Final formula: C^{R}(n,r) = (n + r - 1)! / r! (n - 1)!

Where:

n = the number of possibilities

r = items to be picked up at once

! – is the factorial symbol

both “r” and “n” should be equal or greater than 0.

12 Aug, 2015