How to solve the PIN problem?

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dc65k2021-02-03 11:30:05

Mathematics

dc65k, 2021-02-03 11:30:05

Hello everyone, can you please tell me how to solve the following problem?
The Personal Identification Number (PIN) of the opening lock consists of a set of 3 different digits from 0 to 9 inclusive. The question is, how many possible variants of PINs are there?

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2 answer(s)

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Wataru, 2021-02-03
@dc65k

If in the condition "three different digits" means that all digits are different, then the answer is the number of combinations of 10 by 3, multiplied by the 3 factorial: C(10,3)*3! = 10 * 9 * 8 = 720.
It is logical: there are 10 options to choose the first digit, 9 - the second (excluding the repetition option), and 8 - the third (minus 2 options for repeating the first and second digits).

R

Rsa97, 2021-02-03
@Rsa97

10 ³