Question

How many three-digit numbers are there with no digit repeated?

Answer 1

Given : 

The three-digit number is required without digit repetition Assume we have three boxes; the first box can be filled with any one of the nine digits (0 not allowed at first place). 

Therefore,

Possibilities are ⁹C₁, the second box can be filled with any one of the nine digits available possibilities are ⁹C₁, the third box can be filled with any one of the eight digits available possibilities are ⁸C₁. 

Hence,

Number of total outcomes possible are ⁹C₁ × ⁹C₁ × ⁸C₁ 

= 9 × 9 × 8 

= 648