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I know these formulae...(multinomial theorem) but how does the coefficient of xr in the expansion give the required answer??

I know these formulae...(multinomial theorem)


but how does the coefficient of xr in the expansion give the required answer??

Grade:11

1 Answers

jitender lakhanpal
62 Points
9 years ago

Dear Siva,

 (x0 + x1 + x2 +x3 ...............xn) this 

x0  represents that a person gets o things , x1  represents that the person gets 1 thing,x2  represents that the person gets 2 things....

similarly upto n things now the above expression is repeated for r persons so expression is raised to power r 

as the total number of things are n so the required coefficient is of xn coefficient of this term will give you the number of ways

in which we distribute n identical things among r persons .as when you multiply the expression the total number of things should not be 

more or less than n as if one person get o things other must get n things and similarly if 1 person get 2 things other may get n-3 and third one may get 1 so the coefficient will give you all the number posiibilities .

 

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