# The total number of 3 digit numbers, whose sum of digits is 10, is

Solution:

Let xyz be 3 digit number

x+y+z = 10 where x ≥1, y ≥0, z ≥0

x-1≥0

Put x-1 = t

t≥0

⇒ t+ y+z = 9

9+3-1C3-1 = 11C2 = 55

But for t = 9, x = 10 not possible

Total numbers = 55 – 1 = 54
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