InterviewSolution
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InterviewSolution
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Find the coefficient of `x^3y^4z^5` in the expansion of `(xy+yz+zx)^6`A. 120B. 20C. 30D. 60 |
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Answer» Correct Answer - d Wehave, `(xy + zyzx)^(6) = sum_(r + s + t )(6!)/(r!s!t!) (xy)^(r)(yz)^(s)(zx)^(t)` `= sum_(r + s + t )(6!)/(r!s!t!) x^(r+t)y^(r+s)z^(s+t)` If the general term in the above expansion contains `x^(3) y^(4) z^(5)`, then `r + t = 3 , r + s = 4 and s + t = 5` Also,` r + s + t = 6` Solving these equations, we get ` r = 1, s = 3, t = 2` ` therefore ` Coefficent of `x^(3) y^(4) z^(5) = (6!)/(1!3!2!) = (6!)/(2!3!) = 60` |
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