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So, the coefficient of x^3*y^6*z^5 in (x+y+z)^14 is | So, the coefficient of x^3*y^6*z^5 in (x+y+z)^14 is | ||
| − | 14!/(3!*6!*5!) = 168168 | + | 14!/(3!*6!*5!) = 168168 --[[User:Msstaffo|Msstaffo]] 21:52, 9 March 2009 (UTC) |
[[Midterm Practice Questions]] | [[Midterm Practice Questions]] | ||
Latest revision as of 16:52, 9 March 2009
2. What is the coefficient of x^3*y^6*z^5 in (x+y+z)^14? Explain in words why your answer is correct.
I'm no good at memorizing arbitrary formulas, but I do know that this uses the multinomial theorem. Correct me if I'm wrong, but according to the theorem I think that the answer to this question would be
n!/(k_1)!*(k_2)!*(k_3)!
Where, in this example
n=14 k_1=3 k_2=6 k_3=5
So, the coefficient of x^3*y^6*z^5 in (x+y+z)^14 is
14!/(3!*6!*5!) = 168168 --Msstaffo 21:52, 9 March 2009 (UTC)
