Question

A six digit number is formed using the digits 1, 2, 3, 5, 5, and 8, each exactly once. What is the probability that the resulting number is divisible by 15?

Answer 1

Remember that if a number is divisible by 15, it must be divisible by the factors of 15, 5 and 3. Also remember that if the sum of the digits of a number is divisible by 3, the number is divisible by 3. So $1+2+3+5+5+8=24$, so all of the six digit numbers are divisible by 3. Additionally, for a number to divisible by 5, it's last digit must be divisible by 5. The probability of this occurring is $2/6=1/3$