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Algebra

Blazing goIITian

Joined:	19 Oct 2007
Post:	362

8 Oct 2008 17:41:54 IST

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The number of wqays

None

The number of ways of division or distribution of n identical things into r different is n+r-1Cr-1 .Prove it.

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Comments (3)

nikhil

Cool goIITian

Joined: 5 Oct 2008

Posts: 92

8 Oct 2008 17:48:34 IST

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nPr AM I RIGHT

anchal singhal

Blazing goIITian

Joined: 21 Aug 2008

Posts: 380

8 Oct 2008 18:22:00 IST

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i think ur ques. is not correct

Priyesh

Blazing goIITian

Joined: 18 Feb 2007

Posts: 1042

8 Oct 2008 18:58:18 IST

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no. of ways of dividing n identical things to r different people(say)

then divisions will vary only with the quantity given to the persons (since things are identical)

so let x1 , x2 ,x3, .......... xR be the quantity given to person 1 person 2,person 3...... & so on till person r resp.

so we have to find the no. of non negative integral solns of x1 + x2 + x3 + ....... + xR = n

which is coeff . of x^n in (1+x+x^2....... + x^n)^r

= coeff. of x^n in[ (1-x^(n+1))/(1-x)]^r

= coeff .of x^n in (1-x)^-r

coeff of x^n in (1 + rC1x + r+1C2x^2 +........... + n+r-1Cnx^n )

= n+r-1Cn = n+r-1Cr-1

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