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Find the coefficient of x^4 in the expan...

Find the coefficient of `x^4` in the expansion of `(1+x+x^2+x^3)^(11)dot`

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Given, expansion `= (1 + x + x^(2) + x^(3))^(11) = [(1 + x) + x^(2) (1 + x)]^(11)`
`= [(1 + x) (1 + x^(2))]^(11) = (1 + x)^(11) (1 + x^(2))^(11)`
Now, above expansion becomes
`= (.^(11)C_(0) + .^(11)C_(1) x + .^(11)C_(2) x^(2) + .(11)C_(3) x^(3) + .^(11)C_(4) x^(4) +....) (.^(11)C_(0) + .^(11)C_(1) x^(2) + .^(11)C_(2) x^(4) + ...)`
`= (1 + 11 x + 55 x^(2) + 165 x^(3) + 330 x^(4) +...) (1 + 11 x^(2) + 55 x^(4) +...)`
`:.` Coefficient of `x^(4) = 55 + 605 + 330 = 990`
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