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Part 1 of 1
Choosing the correct counting method depends on whether the arrangement order matters. Use permutations P(n, k) = n! / (n - k)! when order is significant, such as assigning specific roles or forming ranked lists.
Use combinations C(n, k) = n! / (k! * (n - k)!) when order is irrelevant, such as selecting an unranked committee or choosing items from a set.
Worked example
A committee of 3 people is chosen from 8 candidates. Order does not matter, so use combinations: C(8, 3) = 8! / (3! * 5!) = (8 * 7 * 6) / (3 * 2 * 1) = 56 ways.
For the exam
1.The number of ways to award gold, silver, and bronze medals among 10 sprinters is calculated using combinations.
2.The combination formula C(n, k) is equal to C(n, n - k) for all valid n and k.
3.The value of C(5, 2) is equal to 10.
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