Let A = left{ {{a₁},,{a₂},,{a₃}.....} right} be a set containing n elements. Two subsets

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6.Permutation and Combination

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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

${}^n{C_2}\ {2^{n - 2}}$

B

${}^n{C_2}\ {3^{n - 2}}$

C

${}^n{C_2}\ {2^n}$

D

None of these

Solution

For $2$ selected elements there is only one options and for rest there will be $3$ options
$=\, ^nC_2\,3^{n-2}$

Standard 11

Mathematics

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