Find the coefficient of `a^3b^4c^5` in the expansion of `(b c+c a+a b)^6dot`

Explanation

To find the coefficient of \( a^3 b^4 c^5 \) in the expansion of \( (bc + ca + ab)^6 \), we can follow these steps:

### Step 1: Identify the General Term
The general term in the expansion of \( (bc + ca + ab)^6 \) can be expressed using the multinomial theorem:
\[ T(\alpha, \beta, \gamma) = \frac{6!}{\alpha! \beta! \gamma!} (bc)^\alpha (ca)^\beta (ab)^\gamma \]
where \( \alpha + \beta + \gamma = 6 \).
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