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  • Question
  • 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

  • Correct Answer
  • 10!/2 

    Explanation

    As A1 speaks always after A2, they can speak only in  1st  to 9th places and 

     

    A2 can speak in 2nd to 10 the places only when A1 speaks in 1st place 

     

    A2 can speak in 9 places the remaining 

     

     A3, A4, A5,...A10  has no restriction. So, they can speak in 9.8! ways. i.e

     

    when A2 speaks in the first place, the number of ways they can speak is 9.8!.

     

    When A2 speaks in second place, the number of ways they can speak is  8.8!.

     

    When A2 speaks in third place, the number of ways they can speak is  7.8!. When A2 speaks in the ninth place, the number of ways they can speak is 1.8!

     

     

     

    Therefore,Total Number of ways they can  speak = (9+8+7+6+5+4+3+2+1) 8! =  9 2 ( 9 + 1 ) 8 !  = 10!/2

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    Permutation and Combination problems


    Search Results


    • 1. 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
    • 2. A box contains 2 blue balls, 3 green balls and 4 yellow balls. In how many ways can 3 balls be drawn from the box, if at least one green ball is to be included in the draw?

    • Options
    • A. 48
    • B. 24
    • C. 64
    • D. 32
    • Discuss
    • 3. In how many ways the word 'SCOOTY' can be arranged such that 'S' and 'Y' are always at two ends?

    • Options
    • A. 720
    • B. 360
    • C. 120
    • D. 24
    • Discuss
    • 4. The number of sequences in which 4 players can sing a song, so that the youngest player may not be the last is ?

    • Options
    • A. 2580
    • B. 3687
    • C. 4320
    • D. 5460
    • Discuss
    • 5. In how many different ways could couples be picked from 6 men and 9 women ?

    • Options
    • A. 26
    • B. 54
    • C. 52
    • D. 28
    • Discuss
    • 6. 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
    • 7. 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
    • 8. 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
    • 9. 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
    • Discuss
    • 10. 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


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