Question

An even 3 digit no is divisible by 5 and 11 .if the sum of its digit is 8 , find no

Answer 1

Let the five-digit numbers be represented by x1x2x3x4x5.

As the digits of these numbers should add up to 43, we have

x1+x2+x3+x4+x5=43(where 1≤xi≤9, xi∈N)

So, the number of such numbers is equal to the coefficient of x43 in (1−x101−x)5=15

As this is a listable amount of numbers so lets just list them

999979997999799979997999999988998899889988999998989898989899989988998989998

Its easy to spot the numbers divisible by 11 which are 97999,99979,98989

So, the required probability comes out to be 315=15