Question

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. $3999960$

Answer 1

The correct option is D

$3999960$

Explanation for the correct option:

Sum of all five-digit numbers by using $1,2,3,4,5$ without repetition is (Sum of all digits) $\times (\mathrm{n}-1)!\times \frac{{10}^{\mathrm{n}}-1}{10-1}$.

Substitute $n=5$.
$$\begin{gathered} S=(1+2+3+4+5)\times (5-1)!\times \frac{{10}^5-1}{10-1} \\ =15\times 4!\times \frac{99999}{9} \\ =15\times 24\times 11111 \\ =3999960 \end{gathered}$$

Therefore, option (D) is correct.