Q. The sum of all five digit numbers that can be formed using the digits 1, 2, 3, 4, 5 when repetition of digits is not allowed, is
A) 366000
B) 660000
C) 360000
D) 3999960
Explanation
(d)
Required sum=(sum of the digits) $(n - 1)!\left( \frac{10^{n} - 1}{10 - 1} \right)$
$= (1 + 2 + 3 + 4 + 5)(5 - 1)!\left( \frac{10^{5} - 1}{10 - 1} \right)$
$= 360\left( \frac{100000 - 1}{9} \right) = 40 \times 99999 = 3999960$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.