Q. The number of natural numbers less than 1000, in which no two digits are replaced, is
A) 738
B) 792
C) 837
D) 720
Explanation
(a)
The number of 1 digit numbers$= 9$
The number of 2 digit non-repeated numbers$= 9 \times 9 = 81$
The number of 3 digit non-repeated number
$= 9 \times {\ ^{9}P}_{2} = 9 \times 9 \times 8 = 648$
$\therefore$ Required number of ways =9+81+648=738
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.