Find the sixth term in the expansion `(y^(1/2)+x^(1/3))^n` , if the binomial coefficient of the third term of the end is `45.`

Explanation

To find the sixth term in the expansion of \((y^{1/2} + x^{1/3})^n\) given that the binomial coefficient of the third term from the end is \(45\), we can follow these steps:

### Step 1: Identify the term structure
The general term in the expansion of \((a + b)^n\) is given by:
\[ T_k = \binom{n}{k-1} a^{n-k+1} b^{k-1} \]
For our case, \(a = y^{1/2}\) and \(b = x^{1/3}\). The \(k\)-th term can be expressed as:
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