HOW many solutions are dere to the equation:

x1+x2+x3+x4+x5=21

where xi=1,2,3,4,5, is a non-negative integer such that

c)0<=x1<=10

d)0<=x1<=3,1<=x2<4,and x3>=15?

kindly give full soln,not simply ans

Printable View

- Oct 28th 2012, 02:22 AMpanelopy123permutation and combination
HOW many solutions are dere to the equation:

x1+x2+x3+x4+x5=21

where xi=1,2,3,4,5, is a non-negative integer such that

c)0<=x1<=10

d)0<=x1<=3,1<=x2<4,and x3>=15?

kindly give full soln,not simply ans - Oct 28th 2012, 05:48 AMPlatoRe: permutation and combination
These are done with generating functions.

d) Expand $\displaystyle \left( {\sum\limits_{k = 0}^{10} {x^k } } \right)\left( {\sum\limits_{k = 1}^4 {x^k } } \right)\left( {\sum\limits_{k = 15}^{20} {x^k } } \right)\left( {\sum\limits_{k = 0}^5 {x^k } } \right)^2 $

The coefficient of $\displaystyle x^{21}$ answers your question. - Oct 28th 2012, 06:58 AMhediRe: permutation and combination
Attached