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I believe the answer is E. Total number of combinations is 6! (720), which will be the denominator. Then total number of combinations of A and B next to each other will be 2! x 5! (i.e., 240) subtracted by the total number of combinations.

This gives up 2/3 (E).
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Total arrangements of A, B, C, D, E, and F in a row = 6!

Arrangements such that A and B are always together = 5!*2!

Probability of A and B are always together = 5!*2!/6! = 1/3

so probability that A and B are not next to each other
= 1 - (Probability of A and B are always together)
= 1-1/3
= 2/3

Answer: Option E
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Hello from the GMAT Club BumpBot!

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