A combination lock has numbers 0-49 on it. How many different 3-digit lock combinations are possible if no digit can be repeated? (HINT: How many numbers are there, including 0 and 49?

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03-11-2022
Mathematics

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A combination lock has numbers 0-49 on it. How many different 3-digit lock combinations are possible if no digit can be repeated? (HINT: How many numbers are there, including 0 and 49?

Sagot :

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MilasY227781 MilasY227781 · Answer 1 · 2022-11-03T00:44:51-04:00

To solve for this problem, we have to understand PERMUTATION. It is different from combination since in Permutation , the order of the numbers matter and repetition is not allowed. The formula for permutation is:

[tex]P(n,r)=\frac{n!}{(n-r)!}[/tex]

In this problem the value of n is 50 since there are 50 numbers from 0 to 49 and the value of r is 3 since it requires 3-digit combinations. Thus,

[tex]P(50,3)=\frac{50!}{(50-3)!}=\frac{50!}{47!}=117,600[/tex]

Answer: There are 117

A combination lock has numbers 0-49 on it. How many different 3-digit lock combinations are possible if no digit can be repeated? (HINT: How many numbers are there, including 0 and 49?

Sagot :

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