# How many natural numbers less than 10^8 are there, whose sum of digits equals 7?

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## How many natural numbers less than 10^8 are there, whose sum of digits equals 7?

 How many natural numbers less than 10^8 are there, whose sum of digits equals 7? How to compute? Also, will such question be asked in DSE/ISI entrances for Masters in econ?
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## Re: How many natural numbers less than 10^8 are there, whose sum of digits equals 7?

 Hi XIPP,The total no. of ways of dividing n identical items among r persons, such that each one can receive 0,1,2 or more items is (n+r-1)C(r-1). x7+x6+x5+x4+x3+x2+x1+x0=7Here n=7,r=8thus ans is 14C7.Not sure about the other question, may be from IGDIR perspective, but still I think other guys here can guide better.  On Mon, Dec 2, 2013 at 12:46 PM, XIPP [via Discussion forum] wrote: How many natural numbers less than 10^8 are there, whose sum of digits equals 7? How to compute? Also, will such question be asked in DSE/ISI entrances for Masters in econ? If you reply to this email, your message will be added to the discussion below: http://discussion-forum.2150183.n2.nabble.com/How-many-natural-numbers-less-than-10-8-are-there-whose-sum-of-digits-equals-7-tp7584287.html To start a new topic under General Discussions, email [hidden email] To unsubscribe from General Discussions, click here. NAML "Woh mara papad wale ko!"
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## Re: How many natural numbers less than 10^8 are there, whose sum of digits equals 7?

 Many many thanks, Aditya. Will you please let me know where did you learn this technique? Also, will you recommend some book for combinatorics?