The total number of three-digit numbers, with one digit repeated exactly two times, is ______.

Question

Aicharya · Accepted Answer

For three digit number we have following cases,

Case I: When digit zero is repeated

Number of numbers $= {}^{9}C_{1} = 9$

Case II: When digit zero is present but not repeated

Number of numbers $= {}^{9}C_{1} \cdot 2! = 18$

Case III: When digit zero is not present

Number of numbers $= 9 \cdot 8 \cdot \frac{3!}{2!} = 216$

Total number of numbers $= 243$

Solution