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Math Help - Probability Distribution

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    Probability Distribution

    Suppose that  n independent trials, each resulting in one of  m possible outcomes  1, \ldots , m with respective probabilities  p_1, \ldots , p_m are performed. Then

     P \{ X_1 = x_1, X_2 = x_2, \ldots, X_m = x_m | \bold{p} \} = \frac{n!}{x_{1}! \cdots x_{m}!} \ p_{1}^{x_{1}} p_{2}^{x_{2}} \cdots p_{m}^{x_{m}} .

    I don't get the following:  \bold{p} is chosen by a uniform distribution of the form:  f(p_1, \ldots, p_m) = \begin{cases} c, \ \ 0 \leq p_i \leq 1, i = 1, \ldots m, \sum_{1}^{m} p_i = 1 \\ 0, \ \ \text{otherwise} \end{cases} leading to the Bose-Einstein distribution  \binom{n+m-1}{m-1}^{-1} .
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