B1. We consider all five-digit numbers. Of these, there are $a$ with the property that the product of the digits is equal to 25, and $b$ with the property that the product of the digits is equal to 15.

Determine $\frac{a}{b}$.
B1. $\frac{1}{2}$ The numbers of which the product of the digits is 25 consist of two fives and three ones. The number of these, $a$, is equal to the number of ways to place the three ones. There is then only one way to place the two fives.

The numbers of which the product of the digits is 15 consist of a three, a five, and three ones. The number of these, $b$, is equal to the number of ways to first place the three ones and then place the three and the five in two ways.

Thus, it holds that $b=2a$, so $\frac{a}{b}=\frac{1}{2}$.