In Mr. English's 6th period class, there are 8 students that like to line up at the door right before the bell rings. How many ways can these 8 students line up at the door?
Question
In Mr. English's 6th period class, there are 8 students that like to line up at the door right before the bell rings. How many ways can these 8 students line up at the door?
Solution
This is a permutation problem. In permutations, the order of arrangement matters.
The formula for permutations is nPr = n! / (n - r)!, where n is the total number of items, and r is the number of items to choose.
In this case, there are 8 students (n = 8) and we are arranging all of them (r = 8).
So, the number of ways these 8 students can line up at the door is 8P8 = 8! / (8 - 8)!
8! means 8 factorial, which is 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320.
(8 - 8)! is 0!, and the value of 0! is 1.
So, 8P8 = 40320 / 1 = 40320.
Therefore, there are 40,320 ways these 8 students can line up at the door.
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