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Combinatorics Difficulty 1.3 Junior Find the answer Canada

Livy must enter a four-digit code to unlock her phone. She knows
that all four digits are different and that each digit is an integer
from $0$ to $9$ inclusive. If she remembers the first
three digits, but forgets the last digit, what is the probability that
she will enter the correct code on her first try?

Pick one

Solution

Each digit of Livy's code is a different integer from $0$ to $9$ inclusive, meaning that there are $10$ possible digits.

Since each digit of the code is different, Livy knows that the last
digit of the code is not equal to one of the first $3$ digits. This leaves $10-3=7$ possible digits from which Livy
will choose the last digit. The probability that Livy will choose the
correct last digit from these $7$ on
her first try is $\dfrac{1}{7}$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.