Question

Find the number of natural numbers less than (or up to) 1000 having different digits.

Answer 1

Count of single-digit numbers: 9
Count of two-digit numbers: ¹⁰P₂ - ⁹P₁
= 90 - 9
= 81
Count of three-digit numbers: ¹⁰P₃ - ⁹P₂
= 720 - 72
= 648
Consequently, the sum is 9 + 81 + 648 = 738.

The final result is 738.