Problem: If a number is selected at random from the set of all five-digit numbers in which the sum of the digits is equal to , what is the probability that this number will be divisible by
Answer Choices:
A.
B.
C.
D.
E.
Solution:
To total , five digits must be one and four 's or two 's and three 's. There are five and ten or a total of such numbers three of which are divisible by . Hence the probability is or . Divisibility by requires that the sum of the first, third, and fifth digits minus the sum of second and fourth, be divisible by ; only and and satisfy this requirement.