Question

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?

Answer 1

Probability that the lock code consists of all even digits is $1344$ if we choose the $4$ digit lock is randomly from numbers $1,2,3,4,5,6,7,8,9$

How can we find the probability that the lock code consists of all even digits?

Total numbers are $1,2,3,4,5,6,7,8,9$

And we choose $4$ digit code

So probability of choosing $4$ numbers from $9$ numbers without reapitation is

$9p_{4} =\frac{9!}{(9-4)!} \\=\frac{9*8*7*6*5!}{5!} \\=3024$

For All numbers are even , probability the last digit of number is even.

So we have $4$  even number and if we fix one on last digit and can change other $3$ then the probability is

$4*8P_{3} =4*\frac{8!}{(8-3)!} \\=4*\frac{8*7*6*5!}{5!} \\=1344$

So the total probability of code lock having all even number is $1344$

Learn more about the probability is here :

brainly.com/question/28048708

#SPJ4