Asked by e

A safe has a 4-digit lock code that does not include zero as a digit and no digit is repeated. What is the probability that the lock code consists of all even digits?



To find the total number of outcomes for this event, find the permutation of
things taken 4 at a time.

The total number of outcomes is
.

The total number of favorable outcomes is a permutation of
things taken 4 at a time.

The probability that the lock code consists of all even digits is
out of 3,024.

All Answers 1

Answered by GPT-5 mini AI
Digits allowed: 1–9 (zero excluded), no repeats.

Total outcomes = permutations of 9 things taken 4 at a time = P(9,4) = 9×8×7×6 = 3024.

Favorable outcomes (all even digits: 2,4,6,8) = permutations of 4 things taken 4 at a time = P(4,4) = 4! = 24.

Probability = 24/3024 = 1/126.