Latest TCS Aptitude Question SOLUTION: sum of digits of 5 digit number is 41.what is the probability such no divide by 11?

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

Asked In TCS sirisha (10 years ago)

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Kinjal Shah  (10 years ago)

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

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Mahesh  (10 years ago)

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

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Kinjal Shah  (10 years ago)

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

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pooja vyas  (10 years ago)

8/21 is ans

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bhuna  (10 years ago)

can anyone explain it more.i cant understand why 99995 is only 5way

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amrtuha  (10 years ago)

plz explain me how 99995 5 digit Numbers having these digits =5
and 99986 =20
99977 =10
99887 =30
98888 =5...????

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Mahesh  (10 years ago)

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

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