<PRE><B>Question 714642</B>
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From the way you worded the question, I would presume that selecting none of the five choices is NOT an option, i.e., every random selection would include at least one of the choices &quot;A&quot; through &quot;E&quot;.  In this case, your answer of 1/31 is spot on.  On the other hand, if not making any selection is a valid option for answering the question, the correct probability would be 1/32 because you would have to calculate:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sum_{r=0}^5\,{{5} \choose {r}}\ =\ 1\ +\ 5\ +\ 10\ +\ 10\ +\ 5\ +\ 1\ =\ 32]


instead of 


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sum_{r=1}^5\,{{5} \choose {r}}\ =\ 5\ +\ 10\ +\ 10\ +\ 5\ +\ 1\ =\ 31]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
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My calculator said it, I believe it, that settles it
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