Jason 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 6 sports will be taking place. If Jason plans to attend one round of each of these events, in how many different orders could he view them?
Question
Jason 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 6 sports will be taking place. If Jason 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. Permutations refer to the arrangement of items in a specific order.
The formula for permutations is:
P(n, r) = n! / (n-r)!
where:
- n is the total number of items,
- r is the number of items to choose,
- "!" denotes a factorial, meaning the product of all positive integers up to that number.
In this case, Jason has 6 sports events to attend, and he plans to attend all of them, so n = r = 6.
So, the number of different orders in which he could view them is:
P(6, 6) = 6! / (6-6)!
= 6! / 0!
= 6 * 5 * 4 * 3 * 2 * 1 / 1 (because 0! is defined to be 1)
= 720
So, Jason could view the events in 720 different orders.
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