Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2012 based on Arrangement of digits.
Let B be the set of all binary integers that can be written using exactly 5 zeros and 8 ones where leading zeros are allowed. If all possible subtractions are performed in which one element of B is subtracted from another, find the number of times the answer 1 is obtained.
Arrangements
Algebra
Number Theory
Answer: is 330.
AIME, 2012, Question 5
Combinatorics by Brualdi
When 1 subtracts from a number, the number of digits remain constant when the initial number has units and tens place in 10
Then for subtraction from B requires one number with unit and tens place 10.
10 there, remaining 1 distribute any of other 11 then answer \({11 \choose 7} = {330}\).
