A 5 digit no. formed by usng 0,1,2,3,4,5 without repitition the prob. that it is divisible by 6 ?

Dear Mayank

a number is divisibe by 3 and 2 then it is divisible by 6

divisibility by 2

digit at unit place must be even

divisibility by 3

 sum of the digit divisible by 3

  so only two combination is possible 1,2,3,4,5   and 0,1,2,4,5 

    for 1,2,3,4,5

    unit place can be filled by 2 ways

    all other 4 places can be filled by 4*3*2*1 ways

 so total ways  = 2*4*3*2*1 = 48 ways

 for  0,1,2,4,5

   0 is at unit place

  all other 4 places can be filled by 4*3*2*1 ways = 24

  0 is not at the unit place

  unit place can be filled by 2 ways

  all other place can be filled 3*3*2*1

 total ways =2* 3*3*2*1 =36

   so  48+ 24+36 = 108  ways

probability = 108/5*5*4*3*2

                     =.18

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