Suppose that you have an urn filled with balls labeled 1 2 3

Suppose that you have an urn filled with balls labeled 1, 2, 3 or 4. There are ten balls labeled 1, twelve balls labeled 2, nine balls labeled 3, and twenty balls labeled 4. Suppose you draw from the urn n times, replacing balls after each draw. For each i in {1,2, 3, 4}, let X_i be the number of balls drawn from the urn that are labeled i. Suppose n = 16. Compute P(X_1 = X_2 = X_3 = X_4). Be sure to explain your reasoning. Now let n be arbitrary. Give a formula for P(X_1 = x_1 = X_2 = x_2, X = x_3, X_4 = x_4) when x_1 + x_2 + x_3 + x_4 = n. Explain your reasoning.

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