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Let we have 20 identical object   and we want to distribute to 6 different person , how many ways are there  that  each person get atleast one  object  ?

solution :   x1 + x2 + x3 +x4 + x5 + x6  =  20 

where  1 $\leq x _{i} \leq 20$

we have to find coefficient of $x^{20}$  in $( x^{1} + x^{2} + x^{3 } +------+x^{20} )$$^6$

= $x^6(1 + x + x^{2} ------ +x^{19})$$^6$

now we have to find  coefficient of $x^{14}$

$\left [ \frac{1-x ^{20}}{1-x} \right ]^{6}$

= 1$\times  (_{14}^{6+14-1}\textrm{C} )  =               _{14}^{19}\textrm{C}$ $x^{14}$

= 11628 

Answer given  =  230229

where  iam wrong 

closed with the note: got it
in Mathematical Logic by Boss (10.5k points)
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@sumit goyal 1 was the given answer wrong here?

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