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What is the coefficient of x2y2z in the expansion of (x+y+z)5? (Hint: count the

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What is the coefficient of x2y2z in the expansion of (x+y+z)5?  (Hint: count the number of different-looking arrangements of the factors.)

Oct 16th, 2017

The expansion is

(x+y+z)^5 = x^5+5x^4y+5x^4z+10x^3y^2+20x^3yz+10x^3z^2+10x^2y^3+30x^2y^2z+30x^2yz^2+10x^2z^3+5xy^4+20xy^3z+30xy^2z^2+20xyz^3+5xz^4+y^5+5y^4z+10y^3z^2+10y^2z^3+5yz^4+z^5

The coefficient of x^2 y^2 z is 30

Apr 12th, 2015

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