@sumit goyal 1 was the given answer wrong here?

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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

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