- #1
gruba
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Homework Statement
Four people are dealing the total amount of money, which is [itex]1000[/itex] monetary units in terms of [itex]100[/itex] monetary units. Count the number of ways for this distribution if:
[itex]1)[/itex] Every person doesn't have to get any money
[itex]2)[/itex] Every person will get at least [itex]100[/itex] monetary units
[itex]3)[/itex] First person will get at least [itex]500[/itex] m.u. and other three people at least [itex]100[/itex] m.u.
Homework Equations
-Combinatorics
The Attempt at a Solution
The problem doesn't state what is the maximum amount of money that each person can get.
Assuming that, in [itex]1)[/itex] every person will get the same amount ([itex]200[/itex] m.u.), the total number of counts would be the coefficient with [itex]x^{1000}[/itex] in [itex](1+x+...+x^{200})^4[/itex].
In [itex]2)[/itex], assuming that the maximum amount for every person is [itex]200[/itex] m.u, the total number of counts would be the coefficient with [itex]x^{1000}[/itex] in [itex](x^{100}+...+x^{200})^4[/itex].
In [itex]3)\Rightarrow x^{500}(x^{100}+...+x^{200})^3[/itex]
What do you think, how to solve this problem?