Solve the following
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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