Ice cream
- Input
- CR(5, 3)
- Expected output
- 35
5 flavors, 3 scoops, with repetition.
combinations with repetition CR(n,r)
Combinations with Repetition — CR(n,r)
CR(n,r) = C(n+r-1, r). Useful when the same element can be chosen multiple times: ice cream flavors, dice rolls, coin distributions.
When to use combinations with repetition?
- Menu of 5 ice cream flavors, choosing 3 scoops with repetition allowed: CR(5,3) = C(7,3) = 35 ways.
- When distributing r identical objects among n distinct boxes, the number of ways is CR(n,r).
Examples
Distribution
- Input
- CR(4, 6)
- Expected output
- 84
6 identical objects in 4 boxes.
Full tool FAQ
A combination is a selection of r elements from a set of n, where the order of selected elements does not matter. For example, choosing 2 fruits from {apple, pear, grape} gives 3 combinations: {apple, pear}, {apple, grape}, {pear, grape}.
Frequently asked questions
Is CR(n,r) always larger than C(n,r)?
Yes, for r ≥ 2 and n ≥ 2, CR(n,r) ≥ C(n,r), since more options are available when repetition is allowed.
Does this page replace official or professional review?
No. It helps explain the scenario and use the tool more safely, but real decisions should consider official sources, full context and qualified guidance when needed.