Question

How many 6-digit numbers can be formed such that the sum of all the digits is equal to 2?

Answer 1

Such a number must consist of four 0s and two 1s, with 1 as the leading digit. There 5 choices of places for the remaining 1, so there are only 5 such numbers.

110 000

101 000

100 100

100 010

100 001