# Finding the ratio of numbers of ways of selecting at least one defective disc to number of ways of selecting no defectives

4 out of 18 discs are defective , if 3 discs are selected determine the ratio of the number of ways of selecting at least 1 defective disc to the number of ways of selecting no defective discs at all.

The answer is 113 : 91

The number of ways of selecting no defective discs is $C(14,3) = 364$.
The number of ways of selecting any three discs is $C(18,3) = 816$.
So the number of ways of selecting at least one defective disc is $816-364 = 452$ (using the idea of a complement) and so the requested ratio is $452:364 = 113:91$.