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Question

Mathematics Question on Combinations

If nC8 = nC2, find nC2.

Answer

It is known that,nCa=  nCb^nC_a= \space^nC_b
⇒a=b  or  n=a+b⇒a=b\space or\space n=a+b
Therefore,nC8  =  nC2,^nC_8\space =\space ^nC_2
⇒n=8+2=10⇒n=8+2=10
∴nC2=  10C2=102!(10−2)!∴ ^nC_2=\space^{10}C_2=\frac{10}{2!\left(10-2\right)!}
=10!2!8!=10×9×8!2×1×8!=45=\frac{10!}{2!8!}=\frac{10\times9\times8!}{2\times1\times8!}=45