Approximating Probabilities

Abstract

Sometimes an approximation is more valuable than an exact answer. For example, consider the following question: A certain association has 4000 members; 2000 of them are men and 2000 are women. Exactly half the members will be randomly chosen to each receive one ticket to a special event; all members have the same chance of getting a ticket. What is the probability that exactly 1000 men and exactly 1000 women get tickets? The answer to the question is quite obviously

$$ \frac{{{{\left( {\begin{array}{*{20}{c}} {2000} \\ {1000} \end{array}} \right)}^2}}}{{\left( {\begin{array}{*{20}{c}} {4000} \\ {2000} \end{array}} \right)}} $$