Question

if the number of subsets with two elements of set p is 10 then find the total no of elements in set p

Answer 1

$\textbf{Given:}$

$\textsf{Number of two elements subset of P is 10}$

$\textbf{To find:}$

$\textsf{The number of elements in the given set P}$

$\textbf{Solution:}$

$\textsf{Let the number of elements in the given set P be n}$

$\textsf{Number of two elements subset of P}$

$\textsf{=Number of ways of selecting 2 elements from given n elements}$

$\implies\mathsf{10=n_{C_2}}$

$\implies\mathsf{10=\dfrac{n{\times}(n-1)}{1{\times}2}}$

$\implies\mathsf{10=\dfrac{n^2-n}{2}}$

$\implies\mathsf{n^2-n=20}$

$\implies\mathsf{n^2-n-20=0}$

$\implies\mathsf{n^2-5n+4n-20=0}$

$\implies\mathsf{n(n-5)+4(n-5)=0}$

$\implies\mathsf{(n+4)(n-5)=0}$

$\implies\mathsf{n=-4,5}$

$\textsf{But n cannot be negative}$

$\mathsf{n=5}$

$\therefore\boxed{\textsf{Total number of elements in P is 5}}$

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