※ 引述《ooopppeeennn (open)》之銘言： : (a) Find the number of n-dight words generated from the alphabet {0,1,2} : in each of which none of the dights appears exactly three times. : (b) Find the number of n-dight words generated from the alphabet {0,1,2,3,4} : in each of which the total number of 0's and 1's is even (a). (e^x-x^3/3!)^n 求x^n/n! 之係數...... x -x x -x (b) e +e 2 x x x e -e x x x (----------) e e e + (---------)e e e 2 2 = 1/4(e^2x+2+e^-2x)e^xe^xe^x + 1/4(e^2x-2+e^-2x)e^xe^xe^x = 1/2e^5x + 1/2e^x ∞ ∞ = 1/2 Σ 5x^n/n! + 1/2Σ x^n/n! n=0 n=0 求 x^n/n! 之係數 = 1/2(5^n+1) --

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