The probability W(n) that an event characterized by a probability p occurs n times in N...

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The probability W(n) that an event characterized by a probability p occurs n times in N trials was shown to be given by the binomial distribution N! W (n) = n!(N – n)!P"(1 – p)N-n Consider a situation where the probability is small (p « 1) and where one is interested in the case n « N. Several approximations can be made to reduce this expression to a simpler form. Show that N!/(N – n)! - N". The probability W(n) that an event characterized by a probability p occurs n times in N trials was shown to be given by the binomial distribution N! W (n) = n!(N – n)!P"(1 – p)N-n Consider a situation where the probability is small (p « 1) and where one is interested in the case n « N. Several approximations can be made to reduce this expression to a simpler form. Show that N!/(N – n)! - N".