Question

The number of natural numbers less than $1000$, in which no two digits are repeated, is equal to:

• A. $738$
• B. $792$
• C. $837$
• D. $720$

Answer 1

The correct option is A

$738$

Explanation for the correct option:

Finding the number of natural numbers less than $1000$, in which no two digits are repeated, is equal to:

Number of $1$ digit Natural numbers that is less than $1000=9$

Number of two digit number in which no two digits are repeated$=9\times 9=81$

(For one's place we have $9$ choice for ten's place we have $9$ choices (one number placed already) )

Number of three digit number in which No. two digit are repeated $=9x9x8=648$

(For hundred place we have $9$choice ($0$ excluded) for ten's place we have $9$ choices & for one's place we have $8$ choices )

Hence, total number less than $1000$ when two-digit numbers are not repeated $=9+81+648=738$

Hence the correct answer is option (A).