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

[XIPP]

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?

[Bankelal]

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=7

Here n=7,r=8

thus 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] <[hidden email]> 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?

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NAML

[XIPP]

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

[Bankelal]

Quant book for CAT by Arun Sharma will serve better for combinatorics and probability, since it helps to develop the intuitive approach to such problems.

Will definitely help you for IGDIR, but don't expect much for ISI. 

On Tue, Dec 3, 2013 at 8:48 AM, XIPP [via Discussion forum] <[hidden email]> wrote:

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

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NAML

[XIPP]

My focus is DSE and ISI as my English is very very weak. Will you please suggest which book (and topics) to follow for DSE/ISI masters econ (Apart from Chiang, Sydsaeter-Hammond and Simon-Blume)? Is the combo of Sydsaeter-Hammond and Simon-Blume enough for DSE/ISI or any further reference needed?

(I have bachelors in commerce and have working knowledge of maths upto 10+2 NCERT level.)

Your suggestion will build up my career.