Question:
If nC8 = nC2, find nC2.
If nC8 = nC2, find nC2.
Updated On: Oct 21, 2023
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Solution and Explanation
It is known that,\(^nC_a= \space^nC_b\)
\(⇒a=b\space or\space n=a+b\)
Therefore\(,^nC_8\space =\space ^nC_2\)
\(⇒n=8+2=10\)
\(∴ ^nC_2=\space^{10}C_2=\frac{10}{2!\left(10-2\right)!}\)
\(=\frac{10!}{2!8!}=\frac{10\times9\times8!}{2\times1\times8!}=45\)
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