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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2017 · Mathematics · Permutation and Combination

Three-digit numbers are formed from the digits 1,2 and 3 in such a...

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?

Options

  1. A1233
  2. B1322
  3. C1323
  4. D1332

Correct answer

D. 1332

Step-by-step solution

Sum of the numbers = Sum of given numbers. (n−1)![100+101+102+…..]Here,sumofthreedigitnumbers=Sumofthenumbers(\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]=(1+2+3)(3−1)![100+101+102]=6×2×1[1+10+100]=12×111=1332\begin{aligned}& =(1+2+3)(3-1)!\left[10^0+10^1+10^2\right] \\ & =6 \times2 \times1[1+10+100] \\ & =12 \times111 \\ & =1332 \end{aligned}
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