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STD 11 - 6. permutation and combination — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 6. permutation and combination4 Marks
MCQ
Let $A = \left\{ {{a_1},\,{a_2},\,{a_3}.....} \right\}$ be a set containing $n$ elements. Two subsets $P$ and $Q$ of it is formed independently. The number of ways in which subsets can be formed such that $(P-Q)$ contains exactly $2$ elements, is
  • A
    ${}^n{C_2}\ {2^{n - 2}}$
  • ✓
    ${}^n{C_2}\ {3^{n - 2}}$
  • C
    ${}^n{C_2}\ {2^n}$
  • D
    None of these
✓

Answer

Correct option: B.
${}^n{C_2}\ {3^{n - 2}}$
b
For $2$ selected elements there is only one options and for rest there will be $3$ options
$=\, ^nC_2\,3^{n-2}$

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