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no of solns of x+y+z=15.My main is concern is how to solve it through multinomial theorem(Why and how it is used like that) please explain in detail

no of solns of x+y+z=15.My main is concern is how to solve it through multinomial theorem(Why and how it is used like that)
please explain in detail

Grade:12

1 Answers

APURV GOEL
39 Points
9 years ago

Here if 0 is allowed then x,y,z can take values from 0 to 15

so now we have to find coefficient of x15 in (1+x+x2......x15)(1+x+x2......x15)(1+x+x2......x15)

by solving with g.p. formula we get (1-x16)3(1-x)-3

Here (1-x16)3 will have no term with x15 ,so we need to find the coefficient of x^15 in (1-x)-3

We have coefficient of x^r in (1-x)-n is given by n+r-1Cr-1 so we get coefficient of x^15 in (1-x)-3 is 3+15-1C15-1 which is 17C3.

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