Question 1176649


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A sign reads “ALABAMA”, a drunk man removed 4 letters and then returned back
randomly into the four empty spaces again. What is the probability that the
sign still reads “ALABAMA”?<pre>
The order he places them on the sign doesn't matter, for if he picked the 4
A's, the sign will read "ALABAMA" regardless of where he puts them, and if he
didn't pick them, it won't spell "ALABAMA", no matter where he puts them.

So there is only 1 way he can succeed, and that's by choosing the 4 A's.

The number of ways he can pick any 4 of the 7 letters is "7 letters choose 4" or
C(7,4) = 35.

So the probability is 1 way out of 35 or 1/35. 

Edwin</pre>