What is the coefficient of x^{2}y^{2}z in the expansion of (x+y+z)^{5}? (Hint: count the number of different-looking arrangements of the factors.)

The formula to find the coefficient of x1^r1 , x2^r2…xk^rk in (x1+x2+⋯+xk)^n is:

n! / (r1! * r2!*…rk!)

Thus coefficient of x2y2z in (x+y+z)^5 is

5! / (2! * 2!* 1!) = 30 (ANSWER)

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