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  4. The probability that in a random arrangement of the letters of the word “FAVOURABLE”, the two ‘A’ do not come together is

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Q. The probability that in a random arrangement of the letters of the word $“FAVOURABLE$”, the two $‘A’$ do not come together is

Probability

Solution:

Total number of arrangements of the letters of the word $“FAVOURABLE$” is $\frac{10!}{2!}$
Now, say $2A$’s as one letter
$\therefore $ Total number of arrangement if ‘$AA$’ consider one letter is $9!$
$\therefore $ Number of ways in which $‘AA$’ never come together is$= \frac{10!}{2!} - 9!$
$\therefore $ Required probability $= \frac{\frac{10!}{2!} - 9!}{\frac{10!}{2!}} = \frac{4}{5}$