sum of digits of 5 digit number is 41.what is the probability such no divide by 11?

• Those 5 digit numbers whose sum of digits is 41 are
  99995 5 digit Numbers having these digits =5
  99986 =20
  99977 =10
  99887 =30
  98888 =5
  Therefore,total such numbers 70
  For a number abcde to be divisible by 11
  (a+c+e)-(b+d)=11
  The possible combination is a+c+e=26 and b+d=11
  Thus, such numbers are (a,c,e)=(8,9,9)
  and (b,d)=(9,6) or (7,8)
  Therefore, for (a,c,e)=(8,9,9) and (b,d)=(9,6)
  Numbers divsible by 11 are (3!/2!)*2! = 6
  Similarly for (b,d)=(7,8)
  Numbers divisible by 11= 6
  Thus, total numbers divisible by 11 = 12
  Hence, Probability = 12/70 = 6/35
• 10 years agoHelpfull: Yes(29) No(0)
• I agree with Kinjal on the total number of numbers that can be formed is 70.
  
  Now, of those numbers,lets look for the numbers which are divisible bhy 11.
  For a number to be divisible by 11, the sums of alternate digits can be same ( which is not possible in this case as total is 41) or the other case, where the difference between the sums should be a multiple of 11.
  
  So, sum of three digits should be 26 and sum of other two digits should be 15.
  
  Ist, 3 rd and 5 th digits should make a total of 26, which is possible only when these three digits are (9, 9, 8), these can be arranged in any order. The number of ways is 3!/2! = 3 ways
  Let the other two digits that have a sum of 15 be 9 and 6, these two can be arranged in 2 ways.So, total six possible numbers. 86999 is one of the examples for these six numbers.
  
  Lets consider the second case where the numbers that have a sum of 15 be (8 and 7), again 8 and 7 can be arranged in 2 ways .And the total number of numbers here is again 3*2 = 6. Example for these six numbers is 97988.
  
  Total 12 numbers.
  The required probability is 12/70 = 6/35
• 10 years agoHelpfull: Yes(5) No(1)
• Those 5 digit numbers whose sum is 41 are:
  99995 numbers having this combination =5
  99986 =20
  99977--->number of 5 digit =10
  99887--->number of 5 digit =30
  98888--->number of 5 digit =5
• 10 years agoHelpfull: Yes(2) No(0)
• 8/21 is ans
• 10 years agoHelpfull: Yes(0) No(1)
• can anyone explain it more.i cant understand why 99995 is only 5way
• 10 years agoHelpfull: Yes(0) No(0)
• plz explain me how 99995 5 digit Numbers having these digits =5
  and 99986 =20
  99977 =10
  99887 =30
  98888 =5...????
• 10 years agoHelpfull: Yes(0) No(0)
• In 99995, 5 can be in any of the five position like 59999, 95999,99599,99959, or 99995
  Similarly, 98888 can be 98888, 89888, 88988, 88898 or 88889
• 10 years agoHelpfull: Yes(0) No(0)