The probability that in the random arrangement of the letters of the word ALPHABET the two A 39 s do...........

Quantitative Aptitude (CDS) Probability

The probability that in the random arrangement of the letters of the word ALPHABET, the two A's does not come together is?

1/2

1/3

3/4

1/4

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Explanation:

The total number of arrangements of the letters of the word ALPHABET is =8!/2!
The number of arrangements when both A's are together=7!
So the number of arrangements in which both A's do not come together =8!/2! -7!
Therefore required probability=(8!/2! -7!)/(8!/2!)
=(8! -7!×2!)/8!
=7!(8-2)/8!
=6/8
=3/4