Build a 3 Scoop Dessert From 5 Flavors

Decision guide

Why this formula fits

This is combination with repetition because the order of scoops does not matter, but the same flavor may appear more than once.

Does order matter? Order does not matter. Mango-pear-mango is the same bowl as pear-mango-mango.

Is repetition allowed? Repetition is allowed because the customer can choose the same flavor more than once.

Worked solution

5 choose 3 with repeats allowed is 35.

1. Inputs: n = 5, r = 3
2. Formula: C(n + r - 1, r) = (n + r - 1)! / (r!(n-1)!)
3. Substitute: C(5 + 3 - 1, 3) = (5 + 3 - 1)! / (3!(5-1)!)
4. Steps: 5,040 / (6 x 24)
5. Result: 5 choose 3 with repeats allowed is 35.