The 7 letters of the word
G L E N E L G
Q. What is the probability that the sequence is the same from right to left and vice-versa.
Clue please, Thanks
$\displaystyle \frac{\boxed{GLE} \ \boxed{N} \ \boxed{ELG}}{\boxed{GLENELG}}$
The denominator can be arranged in $\displaystyle \frac{7!}{2^3} = 630$ ways.
$\displaystyle \boxed{GLE}$ can be arranged in $\displaystyle 3! = 6$ ways.
The numerator can basically be arranged in $\displaystyle \frac{2!}{2} = 1$ way. (Because the N has to remain in the middle, thus 2!. The first and third terms, as boxed in the numerator, are the same, so we have to divide by 2.)
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Thus the probability is: 6\630 = 1\105
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