What will be the probability that the number has sum of all its digits 25 ?

Question

A non negative number having all distinct digits is such that the product of all digits of the number is 504.
What will be the probability that the number has sum of all its digits 25 ?

Answer 1

Factors are (prime)
2 2 2 3 3 7
Since all digits are distinct so possible factors are
1 2 3 4 6 7
1 2 4 9 7
1 3 4 6 7
1 8 9 7
2 3 4 6 7
2 4 9 7
3 4 6 7
8 9 7

Possible combinations - 8
Favorable combination (with sum as 25 i.e. 1 8 9 7) - 1

Probability = 1/8