Question

Elijah forgot his pass code for a certain website. He knows it is made up of 3 digits and no digit can be repeated. If he randomly chooses 3 different digits, what is the probability that he chooses his pass code?

Answer 1

He has 10 choices for the 1st digit.
He has 9 choices for the 2nd digit.
He has 8 choices for the 3rd digit.
10x9x8 means he has one in 720 probability.

Answer 2

3 digits, there are 10 digits: 0, 1, ..., 9. Order matters 123 is a different code than 321, then

Possible codes: 10 * 9 * 8 = 720, since it can not be repeated.

If he chooses one code:

P = 1 / 720 = 0.138 %

Probably, 1/720 is the best way to write the answer since it shows what it means.