Question

If the number of terms in the expansion `(1+2x-3y+4z)^(n)` is `286`, then find the coefficient of term containing `xyz`.

Answer 1

Correct Answer - `-17280`
Number of term in the expansion
`= .^(n+4-1)C_(4-1) = .^(n+3)C_(3) = ((n+3)(n+2)(n+1))/(3!)`
According to the question,
`((n+3)(n+2)(n+1))/(3!) = 286`
`:. n = 10`
So, the term containing `(xyz)` is `(10!)/(7!!!!!!!!) (1)^(7) (2x)^(1) (-3y)^(1)(4z)^(1)`
`= -17280 xyz`.
Therefore, the required coefficient is `- 17280`.