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

NDA 2017 · Mathematics · Permutation and Combination

Let A=\ 1,2,3,4,5,6,7,8,9,10\ . Then the number of subsets of A...

Let A={1,2,3,4,5,6,7,8,9,10}A=\{1,2,3,4,5,6,7,8,9,10\}. Then the number of subsets of A containing two or three elements is

Options

  1. A45
  2. B120
  3. C165
  4. D330

Correct answer

C. 165

Step-by-step solution

Given, A{1,2,3,4,5,6,7,8,9,10}\mathrm{A}\{1,2,3,4,5,6,7,8,9,10\} Set AA has 10 elements. Number of sub sets Containing 2 and 3 elements is Number of sub sets Containing 2 and 3 elements is 10c2+10c310c2+10c3=(10×92)+(10×9×83×2)\begin{aligned} & 10_{c_2}+10_{c_3} \\ & 10_{c_2}+10_{c_3}=\left(\frac{10 \times 9}{2}\right)+\left(\frac{10 \times 9 \times 8}{3 \times 2}\right)\end{aligned}=45+120=165$
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