Solve the following equation:
$C_{m + 1}^{n + 1} : C_{m}^{n + 1} : C_{m - 1}^{n + 1} = 5 : 5 : 3$

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Solution

$^{n + 1} C_{m + 1} :^{n + 1} C_{m} :^{n + 1} C_{m - 1} = 5 : 5 : 3$

$\frac{1}{(m + 1) m} : \frac{1}{m} : 1 = 5 : 5 : 3$

$1 : (m + 1) : m (m + 1) = 5 : 5 : 3$

$⟹ \frac{1}{m + 1} = 1$
$⟹ m = 0$

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