SOLUTION: A combination lock has the integers 1 through 20 on its dial. Opening the lock requires a combination consisting of 3 of these integers, all different from one another and in a par

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Question 1209380: A combination lock has the integers 1 through 20 on its dial. Opening the lock requires a combination consisting of 3 of these integers, all different from one another and in a particular order. How many different combinations are possible for this lock?

Answer by math_tutor2020(3816) About Me  (Show Source):
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Answer: 6840

Work Shown:
20*19*18 = 6840

Explanation:
Technically it should be called a permutation lock since order matters in a permutation.
There are 20 choices for the first slot, 19 choices for the next, and 18 choices for the final slot. This countdown is happening since we cannot repeat values.
Multiply those values to get the final answer.
Another way to reach this answer is to use the nPr permutation formula with n = 20 and r = 3.