There are 10 projects that made it to the final round of the science competition. In how many different orders can the judges rank these projects?
Question
There are 10 projects that made it to the final round of the science competition. In how many different orders can the judges rank these projects?
Solution
The number of different orders in which the judges can rank the projects is determined by the number of permutations of the 10 projects.
A permutation is an arrangement of objects in a specific order. The number of permutations of n objects is given by n factorial, denoted as n!.
So, for 10 projects, the number of permutations is 10!, which is calculated as:
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800
So, the judges can rank the 10 projects in 3,628,800 different ways.
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