Question

Quinn, Joe, James, and Sean sit in the four desks in the last row of desks. Each day they sit in a different order. How many days can they do this before they repeat a seating pattern?

Answer 1

24

Explanation:

The number of permutations of 4 items taken 4 at a time is 4! = 24.

They can go 24 days without a repeated pattern.

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4! = 4×3×2×1 = 24

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Any of the four can sit at the first desk; any of the remaining 3 at the next desk; either of the remaining 2 at the next desk. The total number of possibilities is the product of the numbers of possibilities at each desk: 4×3×2×1 = 24.