If a seven digit number formed with distinct digits 4,6 , 9,5,3, x and y is divisible by 3 , then the number of such ordered pairs (x, y) is

Step-by-step solution

Recall that when a number is divisible by 3 then sum of its digits is also divisible by 3 . So, we have 4+6+9+5+3+x+y=3 k for some k Z 27+(x+y)=3 k So, (x+y) is also some multiple of 3 . Since all the seven digit numbers is to have distinct therefore x and y must be chosen from 0,1,2,7,8 such that (x+y) is some multiple of 3 . If x=0 , then there is no possibility for y If x=1 , then y=2,8 (1,2),(1,8) If x=2 , then y=1,7 (2,1),(2,7) If x=7 , then y=2,8 (7,2),(7,8) If x=8 , then y=1,7 (8,1),(8,7) 8 pairs are possibl