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by rupsk » Sat Sep 10, 2011 5:42 pm
How many positive integer less than 10000 are there in which the sum of digits is 5
(A) 31 (B) 51(C) 56(D) 62(E) 934.
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by knight247 » Sat Sep 10, 2011 6:53 pm
We will keep our upper barrier as 9,999 inclusive. I prefer doing it this way.

Now, if the sum of digits have to add up to 5 we have the following options

0005 which can be arranged in 4!/3!=4 Ways
2003 which can be arranged in 4!/2!=12 Ways
1130 which can be arranged in 4!/2!=12 Ways
4100 which can be arranged in 4!/2!=12 ways
1121 which can be arranged in 4!/3!=4 Ways
2210 which can be arranged in 4!/2!=12 Ways

Summing up we get 56 ways. Hence[spoiler] C[/spoiler]
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by GMATGuruNY » Sun Sep 11, 2011 3:13 am
This is a distribution question. The quickest approach is to use the separator method. I posted a solution here:

https://www.beatthegmat.com/experts-any- ... tml#362526
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by rupsk » Sun Sep 11, 2011 12:48 pm
@GMATGuru
I am not able to understand your separator method. Why u have taken 5 digit and how you have separated its confusing to me, please help in understanding it.

@Knight
How you have taken denominator value please explain me that.
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