Worked example
There are 120 ways to choose an unordered group of three people from ten. There are 720 ways to assign three distinct roles from ten people. The difference is whether changing the order makes a new outcome.
Method
Without replacement, permutations count n!/(n−r)! and combinations divide that result by r!. For ten people and three places: 10 × 9 × 8 = 720 ordered outcomes; divide by 3 × 2 × 1 to obtain 120 groups.
Check the assumptions
Use combinations for a committee with identical membership roles. Use permutations for first, second, and third places. These formulas assume distinct choices without replacement; repeated selections require a different model.
Try your own values
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For a shorter explanation, read the direct answer. Compare the underlying quantities in the comparison.
