Question:
If mC1 = nC2 , then
(a) 2 m = n
(b) 2 m = n (n + 1)
(c) 2 m = n (n − 1)
(d) 2 n = m (m − 1)
Solution:
(c) 2 m = n (n − 1)
${ }^{m} C_{1}={ }^{n} C_{2}$
$\Rightarrow \frac{m !}{1 !(m-1) !}=\frac{n !}{2 !(n-2) !}$
$\Rightarrow \frac{m(m-1) !}{(m-1) !}=\frac{n(n-1)(n-2) !}{2(n-2) !}$
$\Rightarrow 2 m=n(n-1)$
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