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Discussion Response Post to: The number of wqays

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Priyesh (1601)

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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

"Imagination is more important than knowledge."

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