permutation and combination

This topic contains 10 replies, has 4 voices, and was last updated by  shruti290 5 years, 4 months ago.

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  • #499

    shruti290
    Participant

    q1.)the number of numbers divisible by 3 tht can be formed by four different even digits is?
    q2.)the no of 4 digit no tht can be made with the digits 1,2,3,4 and 5 in which at least 2 digits are identical?


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  • #501

    rohit pandey
    Participant

    for q2
    at least 2 digits same means
    we take cases for
    1.2 same digits
    2.3 same digits
    3.4 same digits

    and add them up

    for case 1-5*4*3*2/2!
    for case 2 – 5*4*3*2/3!
    for case 3 – 5*4*3*2/4!
    now add all of them up
    this is a probable solution


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    • #503

      abhisheksharma12593
      Participant

      atleast 2 are identical means either 2 are identical or 3 are identical or 4 are identical
      no of ways if 2 are identical are 5*4*3*2/2!
      no of ways if 3 are identical are 5*4*3/3!
      no of ways if 4 are identical are 5*4*3*2/4!
      adding all three we get 60+20+5=85 ways
      our answers are same but i didn’t follow youe method rohit


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      • #506

        abhisheksharma12593
        Participant

        *CORRECTION TO ABOVE REPLY
        atleast 2 are identical means either 2 are identical or 3 are identical or 4 are identical
        no of ways if 2 are identical are 5*4*3*2/2!
        no of ways if 3 are identical are 5*4*3*2/3!
        no of ways if 4 are identical are 5*4*3*2/4!
        adding all three we get 60+20+5=85 ways
        our answers are same but i didn’t follow your method rohit
        what you are saying is that either 1,2 or 2,3 or 3,4 are identical…plz explain this


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  • #502

    rohit pandey
    Participant

    for q 1

    even digits are 0 , 2 , 4 ,6 ,8

    so probable 4 digits are 1.0246=0+2+4+6=12
    2.2468=2+4+6+8=20
    3.4680=4+6+8+0=18
    4.6802=6+8+0+2=16
    5.8024=8+0+2+4=14

    only option 1 and option 3 is divisible by 3

    so permutation of option1=4!-3!
    ( we do -3! factorial because we need 4 digit numbers and thus we fix 0 at fourth place and form permutations and subtract it from total permutations}
    and
    permutation of option2=4!-3! {same thing again}
    this is a probable answer

    where did you get this question?


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    • #509

      shruti290
      Participant

      i did not follow what u said and the correct ans is 505 i forgot to mention and i got it
      basically the question says tht atleast 2 didigts are identical which is just another way of saying tht at least one digit is repeated therefore the answe is
      5^4-5!
      that is the total no of ways- no digit repeated


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      • #513

        abhisheksharma12593
        Participant

        i didn’t get this at all…….let admin come to rescue!!!


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    • #510

      shruti290
      Participant

      the correct answer is 36 and yours is 18


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    • #518

      shruti290
      Participant

      Why did u take o ?
      And tell me one thing it says “the no of numbers” so shouldn’t we take the one digit two digit three and four digit no’s As well and since it says diff even do digits therefore we cannot exceed beyond four digits ?


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  • #526

    admin
    Keymaster

    For q1, Rohit is right.. and Shruti, his answer is 36 indeed (not 18)

    For q2, Shruti is right
    #ways at least 2 identical = total ways – #ways none identical
    …this is the same approach of using the complement, which is often easier


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    • #535

      shruti290
      Participant

      but sir why did he take 0?


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