View source for 2. What is the coefficient of x^3y^6z^5 in (x+y+z)^14? Explain in words why your answer is correct. - Rhea

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

[[Midterm Practice Problems]]