If ^{n} C_{8}=,^{n} C_{2}, find ^{n} C_{2}.

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6.Permutation and Combination

easy

If $^{n} C_{8}=\,^{n} C_{2},$ find $^{n} C_{2}.$

A

$45$

B

$45$

C

$45$

D

$45$

Solution

It is known that, $^{n} C_{a}=\,^{n} C_{b} \Rightarrow a=b$ or $m=a+b$

Therefore,

$^{n} C_{8}=\,^{n} C_{2} \Rightarrow n=8+2=10$

$\therefore\,^{n} C_{2}=\,^{10} C_{2}=\frac{10 !}{2 !(10-2) !}=\frac{10 !}{2 ! 8 !}=\frac{10 \times 9 \times 8 !}{2 \times 1 \times 8 !}=45$

Standard 11

Mathematics

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