If one threedigit number 0 cannot be a left digit is chosen

If one three-digit number (0 cannot be a left digit) is chosen at random from all those that can be made from the following set of digits, find the probability that the one chosen is not a multiple of 5. {0,1,2,3,4,5,6,7}.

What is the probability that the one chosen is not a multiple of 5.

Solution

I am assuming that the digits can be repeated since it is not given in the problem

Total Possible Numbers = First Digit * Second Digit * Third Digit

=> 7(any number excluding zero) * 8 (any of the above numbers) * 8 (any of the above numbers)

=> 7 * 8 * 8

=> 448 numbers

Number divisible by 5 (whose last digit is either 0 or either 5)

=> 7 * 8 * 2

=> 112 digits

Probability that one chosen is not a multiple of 5 = 1 - P(it is a multiple of 5)

=> 1 = 112/448

=> 1 - 1/4

=> 3/4 = 0.75