# Lottery also comes in numbers!

A lottery comes in form of 6-digit numbers from $$000000$$ to $$999999$$.

Let us call a lottery lucky if the sum of the first 3 digits are equal to the last 3 digits. For example, $$456177$$ is lucky because $$4+5+6 = 1+7+7$$.

And let us call a lottery good if the sum of all digits is 27. For example, $$345456$$ is good because $$3+4+5+4+5+6 = 27$$.

If the number of different possible lotteries that are lucky is $$a$$, and the number of different possible lotteries that are good is $$b$$, find the value of $$a-b$$.

This question is from Thailand Math POSN, Combinatorics.

×