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MATHCHAPTER E The Multinominal Distribution and Stirling's Approximation PROBLEMS AND SOLUTIONS E-1. Use Equation E.3 to write the expansion of Use Equation E.4 to do the same thing. Using Equation E.3, we can write = = Equation E.4 gives the same result. E-2. Use Equation E.6 to write out the expression for Compare your result to the one that you obtain by multiplying by Using Equation E.6, we can write = 2!0!0! 2! + + 1!1!0! 2! + 2! + 0!2!0! 2! + 2! We obtain the same result when we multiply (x + + by (x + y + z). E-3. Use Equation E.6 to write out the expression for Compare your result to the one that you obtain by multiplying from Problem E-2 by itself. Using Equation E.6, we can write 444* = 4!0!0! 4! + 3!1!0! 4! + 3!0!1! 4! + 2!2!0! 4! + 2!0!2! 4! 2!1!1! 4! + 1!3!0! 4! + 1!0!3! 4! + 1!2!1! 4! + 1!1!2! 4! 171

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