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 non - zero digits

The non - zero digits are 1, 2, 3, 4, 5, 6, 7, 8, 9. So, to find the total number of outcomes for the 4 - digit lock code, we find the permutation of 9 things taken 4 at a time. The formula for permutations is $P(n,r)=\frac{n!}{(n - r)!}$. Here, $n = 9$ and $r=4$, so $P(9,4)=\frac{9!}{(9 - 4)!}=\frac{9!}{5!}=9\times8\times7\times6=3024$.

Step2: Determine non - zero even digits

The non - zero even digits are 2, 4, 6, 8. The total number of favorable outcomes is a permutation of 4 things taken 4 at a time. Using the permutation formula $P(n,r)$ with $n = 4$ and $r = 4$, we have $P(4,4)=\frac{4!}{(4 - 4)!}=\frac{4!}{0!}=4!=4\times3\times2\times1 = 24$.

Step3: Calculate probability

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

Answer:

The first blank: 9; the second blank: 3024; the third blank: 4; the fourth blank: 24.