# Math Help - Permutations

1. ## Permutations

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.

2. Originally Posted by Misa-Campo
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.

$\frac{\boxed{GLE} \ \boxed{N} \ \boxed{ELG}}{\boxed{GLENELG}}$

The denominator can be arranged in $\frac{7!}{2^3} = 630$ ways.

$\boxed{GLE}$ can be arranged in $3! = 6$ ways.

The numerator can basically be arranged in $\frac{2!}{2} = 1$ 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.)