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  • Question
  • How many different words can be made using the letters of the word ' HALLUCINATION ' if all constants are together?


  • Options
  • A. 129780
  • B. 1587600
  • C. 35600
  • D. None of these

  • Correct Answer
  • 1587600 

    Explanation

     H   L   C   N    T    A   U   I   O

     

          L        N          A        I

     

    There are total 131 letters out of which 7 are consonants and 6 are vowels. Also ther are 2L's , 2N's, 2A's and 2I's.

     

    If all the consonants  are together then the numberof arrangements =  7 ! 2 ! x 1/2! .

    But the 7 consonants  can be arranged themselves in   7 ! 2 !  x 1/2! ways. 

     

    Hence the required number of ways =  7 ! 2 ! 2 ! 2 = 1587600

  • Tags: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk, Analyst

    Permutation and Combination problems


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    • 1. There are 5 novels and 4 biographies. In how many ways can 4 novels and 2 biographies can be arranged on a shelf ?

    • Options
    • A. 26100
    • B. 21600
    • C. 24000
    • D. 36000
    • Discuss
    • 2. How many arrangements of the letters of the word ?BENGALI? can be made if the vowels are never together.

    • Options
    • A. 120
    • B. 640
    • C. 720
    • D. 540
    • Discuss
    • 3. In How many ways can the letters of the word 'CAPITAL' be arranged in such a way that all the vowels always come together?

    • Options
    • A. 360
    • B. 720
    • C. 120
    • D. 840
    • Discuss
    • 4. If A1, A2, A3, A4, ..... A10 are speakers for a meeting and A1 always speaks after, A2 then the number of ways they can speak in the meeting is

    • Options
    • A. 9!
    • B. 9!/2
    • C. 10!
    • D. 10!/2
    • Discuss
    • 5. Out of 6 green ball, 4 blue ball, in how many ways we selectone or more balls ?

    • Options
    • A. 42
    • B. 34
    • C. 31
    • D. 22
    • Discuss
    • 6. If a+b+c = 21, what is the total number of non - negative integral solutions?

    • Options
    • A. 123
    • B. 253
    • C. 321
    • D. 231
    • Discuss
    • 7. The number of signals that can be generated by using 5 differently coloured flags, when any number of them may be hoisted at a time is:

    • Options
    • A. 235
    • B. 253
    • C. 325
    • D. None of these
    • Discuss
    • 8. A Cricket team of 23 people all shake hands with each other exactly once. How many hand shakes occur ?

    • Options
    • A. 142
    • B. 175
    • C. 212
    • D. 253
    • Discuss
    • 9. There are 3 sections with 5 questions each. If four questions are selected from each section, the chance of getting different questions is ?

    • Options
    • A. 1000
    • B. 625
    • C. 525
    • D. 125
    • Discuss
    • 10. Some children goto ice-cream shop. 9 flavours are available there. Each child takes a cone with two different flavours. No two children take same combination and they have taken all such possible combinations. How many children went to ice cream shop ?

    • Options
    • A. 28
    • B. 56
    • C. 44
    • D. 36
    • Discuss


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