Question

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

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

Answer 1

Answer: (A)

$738$

Numbers less than $1000$ are one digit no., two digits numbers and three digits number.

No. of one digit number $=9$

No. of two digit number in which $=9\times 9=81$

no. two are repeated

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

No. of three digit number in which No. two digit are repeated $=9\times 9\times 8$

$=648$

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

$\therefore$ Total number less than 1000 in which no. two digits are repeated are : $=9+81+648$

$=738$