The probability that in a random arrangement of the letter of the word 'UNIVERSITY', the two I's do not come together is:

Question

The probability that in a random arrangement of the letter of the word 'UNIVERSITY', the two I's do not come together is: (A) (4/5) (B) (1/10) (C) (9/10) (D) (1/5)

Tardigrade Admin · Accepted Answer

The total number of arrangement of the letters in the word ‘UNIVERSITY’ is

\frac{10 !}{2 !}

(

∵

Total letters = 10, I occurs twice)
Now, if 2I’s occurs together, then regard 2I’s as one letter.
Then, total number of arrangement in which 2I’s are not together

= \frac{10 !}{2 !} - 9!

Hence, required prob

= \frac{\frac{10 !}{2 !} - 9 !}{\frac{10 !}{2 !}} = 1 - \frac{9 ! 2 !}{10 !} = 1 - \frac{1}{5} = \frac{4}{5}

Q. The probability that in a random arrangement of the letter of the word 'UNIVERSITY', the two I's do not come together is:

$\frac{4}{5}$

$\frac{1}{10}$

$\frac{9}{10}$

$\frac{1}{5}$

Q. The probability that in a random arrangement of the letter of the word 'UNIVERSITY', the two I's do not come together is:

54​

101​

109​

51​

$\frac{4}{5}$

$\frac{1}{10}$

$\frac{9}{10}$

$\frac{1}{5}$