Q157 / 270 · NDA 2017 (Phase 1) · Mathematics
Three-digit numbers are formed from the digits 1,2 and 3 in such a way that the digits are not repeated. What is the sum of such three-digit numbers?
- A1233
- B1322
- C1323
- Correct answerD1332
Solution
Sum of the numbers $=$ Sum of given numbers.
$(\mathrm{n}-1)!\left[10^0+10^1+10^2+\ldots . .\right]$
Here, sum of three digit numbers $=$ Sum of the numbers $(3-1)!\left[10^{\circ}+10^1+10^2\right]$
$\begin{aligned}
& =(1+2+3)(3-1)!\left[10^0+10^1+10^2\right] \\
& =6 \times 2 \times 1[1+10+100] \\
& =12 \times 111 \\
& =1332
\end{aligned}$
Hence, the correct answer is option: 'D'.