a safe has a 4 - digit lock code that does not include zero as a digit and no digit is repeated. what is the…

Explanation:

Step1: Determine available digits

The digits are 1 - 9 (9 non - zero digits).

Step2: Calculate total number of outcomes

The formula for permutations is $P(n,r)=\frac{n!}{(n - r)!}$. Here, $n = 9$ and $r=4$. So $P(9,4)=\frac{9!}{(9 - 4)!}=\frac{9!}{5!}=9\times8\times7\times6=3024$.

Step3: Determine favorable digits

The non - zero even digits are 2, 4, 6, 8 (4 digits).

Step4: Calculate favorable number of outcomes

Using the permutation formula with $n = 4$ and $r = 4$, $P(4,4)=\frac{4!}{(4 - 4)!}=\frac{4!}{0!}=4\times3\times2\times1 = 24$.

Step5: Calculate probability

The probability is the number of favorable outcomes divided by the total number of outcomes. So the probability is $\frac{24}{3024}=\frac{1}{126}$.

Answer:

The total number of outcomes for this event is found by finding the permutation of 9 things taken 4 at a time. The total number of outcomes is 3024. The total number of favorable outcomes is a permutation of 4 things taken 4 at a time. The probability that the lock code consists of all even digits is 24 out of 3024.