Question 12: Given 5 numbers 0≠a,b,c,d,e∈Z. How many fractions can be formed in all with the numerator and denominator of the given 5 numbers. Know that numerator and denominator must be different

+ Fractions with number a: choose one more number out of the other 4 and get the numbers \( \frac{a}{b},\frac{a}{c},\frac{a}{d},\frac{a}{e},\frac{b}{a},\frac{ c}{a},\frac{d}{a},\frac{e}{a}\)

+ Numbers with numbers b, c, d, e are similar. Notice that the fractions overlap.

So there are only 20 different fractions