Combinations count unordered groups: nCr = n! / (r!(n − r)!). Order does not matter. If order does matter, you want permutations, in permutations versus combinations.
Choose, do not arrange
A committee of 3 from 10 people is C(10, 3) = 120. A president, treasurer, and secretary from those 10 is a permutation. Mutually exclusive events are a probability neighbor, in mutually exclusive events.
Series sums are a different counting formula, in arithmetic series sum. The short list is in ACT Math formulas.
The bottom line
Unordered groups: nCr. Factorials in, identical orders out.
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