Q153 / 270 · NDA 2024 (Phase 1) · Mathematics
What is the sum of all four digit numbers formed by using all digits $0,1,4,5$ without repetition of digits?
- A44440
- B46460
- C46440
- Correct answerD64440
Solution
Sum of all four digit number start with 1
$\begin{aligned}
& =1 \times 6 \times 1000+18 \times 100+18 \times 10+18 \\
& =6000+1800+180+18=7998
\end{aligned}$
Sum of all four digit numbers start with 4
$\begin{aligned}
& =4 \times 6 \times 1000+12 \times 100+12 \times 10+12 \\
& =24000+1200+120+12=25332
\end{aligned}$
Sum of all four digit numbers start with 5
$\begin{aligned}
& =6 \times 5 \times 1000+10 \times 100+10 \times 10+10 \\
& =30000+1000+110=31110
\end{aligned}$
$\therefore$ Required sum $=7998+25332+31110=64440$.
Hence, the correct answer is option: 'D'.