Question

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

• A. $738$
• B. $585$
• C. $837$
• D. $720$

Answer 1

Answer: (B)

Number of one digit natural number $=9$
Number of two digit natural numbers with different digits $=9\times 8$
Number of three digit natural number with different digits $=9\times 8\times 7$
Total number of natural number $<1000$ with number of digit is repeated $=9+72+504$
$=585$.