Find the unknown value : ^ n C_ 2 =28 - Vidyadip

Question

Find the unknown value : ${ }^{n} C_{2}=28$

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Answer

${ }^n C_2=28$
$ \therefore \frac{n !}{2 !(n-2) !}=28$
$ \therefore \frac{n(n-1)(n-2) !}{2 \times(n-2) !}=28$
$ \therefore \mathrm{n}(\mathrm{n}-1)=28 \times 2$
$ \therefore \mathrm{n}(\mathrm{n}-1)=56$
$ \therefore \mathrm{n}(\mathrm{n}-1)=8 \times 7$
$ \therefore \mathrm{n}(\mathrm{n}-1)=8(8-1)$
$ \therefore \mathrm{n}=8$

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