Consider the set A= 1,2,3, , 30 . The number of ways in which one can choose three distinct numbers from Aso that the product of the chosennumbers is divisible by 9 is

Step-by-step solution

We define the following subsets of set A : X =9,18,27 (divisible by 9) Number of elements =3 Y =3,6,12,15,21,24,30 ( divisible by 3 but not by 9 ) Numher if elements =7 Z = all the remaining elements of set A (not divisible by 3 ) Number of elements =20 Number of ways of choosing 3 distinct numbers such that their product is NOT divisible by 9 : (I) Choose any 3 numbers from subset Z = ²⁰ C ₃=1140 (II) Choose any 2 numbers from subset Z and any 1 number from subset Y = ²⁰ C ₂ ⁷ C ₁=1330 Total number of ways of choo