Austen won a trip to the upcoming Winter Olympics and needs to plan which events to attend. During the first week of competition, preliminary rounds of 5 sports will be taking place. If Austen plans to attend one round of each of these events, in how many different orders could he view them?
Question
Austen won a trip to the upcoming Winter Olympics and needs to plan which events to attend. During the first week of competition, preliminary rounds of 5 sports will be taking place. If Austen plans to attend one round of each of these events, in how many different orders could he view them?
Solution
This is a permutation problem. Austen has 5 events to attend and the order in which he attends them matters.
The formula for permutations is nPr = n! / (n - r)!, where n is the total number of options, r is the number of options chosen at a time, and "!" denotes a factorial, which means to multiply a number by every number less than it down to 1.
In this case, n = 5 (the total number of events) and r = 5 (the number of events Austen is attending), so the formula becomes:
5P5 = 5! / (5 - 5)!
= 5! / 0!
Since 0! is defined as 1, this simplifies to:
= 5!
= 5 * 4 * 3 * 2 * 1
= 120
So, Austen could view the events in 120 different orders.
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