Question

Five students are competing in a race. In how many different

could the five students place in the race?
combinations

Answer 1

120

Explanation:

• we need to find the number of the possible orderings

of this five students.

•• which we can simulate to a permutation

of 5 objects.

••• and we know that The number of permutations

of 5 distinct objects is 5!.

5! = 5×4×3×2×1 = 120

there are six permutations of the set {1, 2, 3}, namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set.

The number of permutations of n distinct objects is n factorial, usually written as n!, which means the product of all positive integers less than or equal to n.