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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2024 · Mathematics · Permutation and Combination

What is the sum of all four digit numbers formed by using all...

What is the sum of all four digit numbers formed by using all digits 0,1,4,50,1,4,5 without repetition of digits?

Options

  1. A44440
  2. B46460
  3. C46440
  4. D64440

Correct answer

D. 64440

Step-by-step solution

Sum of all four digit number start with 1 =1×6×1000+18×100+18×10+18=6000+1800+180+18=7998\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 =4×6×1000+12×100+12×10+12=24000+1200+120+12=25332\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 =6×5×1000+10×100+10×10+10=30000+1000+110=31110\begin{aligned} & =6 \times 5 \times 1000+10 \times 100+10 \times 10+10 \\ & =30000+1000+110=31110 \end{aligned}\thereforeRequiredsumRequired sum=7998+25332+31110=64440$.
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