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Question
If mC1 = nC2 , then
Options
2 m = n
2 m = n (n + 1)
2 m = n (n − 1)
2 n = m (m − 1)
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Solution
2 m = n (n − 1)
mC1 = nC2
\[\Rightarrow \frac{m!}{1! \left( m - 1 \right)!} = \frac{n!}{2! \left( n - 2 \right)!}\]
\[ \Rightarrow \frac{m \left( m - 1 \right)!}{\left( m - 1 \right)!} = \frac{n \left( n - 1 \right) \left( n - 2 \right)!}{2 \left( n - 2 \right)!}\]
\[ \Rightarrow 2m = n \left( n - 1 \right)\]
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