2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Probability

JEE Main & Advanced Mathematics Probability Question Bank Self Evaluation Test - Probability-I

  • question_answer
    The probability that in the random arrangement of the letters of the word 'UNIVERSITY' the two I's does not come together is

    A) \[\frac{4}{5}\]

    B) 1/5

    C) 1/10

    D) 9/10

    Correct Answer: A

    Solution :

    [a] Total no. of arrangements of the letters of the word UNIVERSITY is \[\frac{10!}{2!}\]. No. of arrangements when both I?s are together \[=9!\] So. The no. of ways in which 2 I?s do not together \[=\frac{10!}{2!}-9!\] \[\therefore \] Required probability \[=\frac{\frac{10!}{2!}-9!}{\frac{10!}{2!}}=\frac{10!-9!2!}{10!}\] \[=\frac{10\times 9!-9!2!}{10!}=\frac{9![10-2]}{10\times 9!}=\frac{8}{10}=\frac{4}{5}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner