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

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 of a lock without all even digits? there to get a lock code with all even digits. there are 3,024 different 4 - digit lock codes. there are to get a lock code without all even digits. the probability of a 4 - digit lock code without all even digits is

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 of a lock without all even digits? there to get a lock code with all even digits. there are 3,024 different 4 - digit lock codes. there are to get a lock code without all even digits. the probability of a 4 - digit lock code without all even digits is

Answer

Explanation:

Step1: Calculate number of all - even - digit codes

The non - zero even digits are 2, 4, 6, 8. The number of ways to arrange 4 non - repeated non - zero even digits for a 4 - digit code is given by the permutation formula (P(n,r)=\frac{n!}{(n - r)!}), where (n = 4) and (r=4). So (P(4,4)=\frac{4!}{(4 - 4)!}=4!=4\times3\times2\times1 = 24).

Step2: Calculate number of codes without all even digits

The total number of 4 - digit lock codes with no zero and no repeated digits is (9\times8\times7\times6=3024) (9 choices for the first digit, 8 for the second, 7 for the third, and 6 for the fourth). The number of codes without all even digits is (3024−24 = 3000).

Step3: Calculate the probability

The probability (P) of getting a 4 - digit lock code without all even digits is (\frac{3000}{3024}=\frac{125}{126}).

Answer:

There are 24 ways to get a lock code with all even digits. There are 3000 ways to get a lock code without all even digits. The probability of a 4 - digit lock code without all even digits is (\frac{125}{126})