Making up Numbers

For it to be divisible by 5, the last digit has to be 5.
The first 3 digits can take on any of the 7 digits. Hence, the number of ways with a last digit of 5 is 7 7 7. The total number of ways to make four digit numbers are 7 7 7 7. The probability that a number is divisible by 5 is 7 7 7/7 7 7 =1/7

A : Number of numbers divisible by 5. P(A)=(Number of numbers divisible by 5.)/(Total number of numbers that can be formed from {1,2,3,4,5,6,7}.)

For the number to be divisible by 5, of the 4 digits the last one should always be 5. As the digits are distinct, the other 3 digits can be chosen from {1,2,3,4,6,7} in 6C3 ways. Covering all possible permutations, the 3 digits can be chosen in 6C3 x 3! ways (rearranging the first 3 digits). The total number of ways to form 4 digit numbers from {1,2,3,4,5,6,7} are 7C4 x 4! (Choosing 4 digits and covering all their possible rearrangements).

Thus, P(A)=(6C3 x 3!)/(7C4 x 4!)=1/7. Therefore, 1+7=8.