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# A committee of fifty politicians is to be chosen from among our one hundred U.S. senators. If the selection is done at random, what is the probability that each state will be represented?

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Given: 50 senators are selected from the 100 U.S. senators. 2 senators are from each state.

Definition permutation (order is important):

$_nP_{r}=\dfrac{n!}{(n-r)!}$

Definition combination (order is not important):

$_nC_{r}=\dfrac{n!}{r!(n-r)!}$

with $n!=n\cdot (n-1)\cdot ...\cdot 2\cdot 1$.

Fundamental counting principle: If one event can occur in $m$ ways and a second event can occur in $n$ ways, the number of ways the two events can occur in sequence is then $m\cdot n$.

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