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Let X denote the number of ways of distributing 7 identical balls to 3 children such that each child gets at least one ball. Then the value of X is equal to _________.
what should I be using here.. ($_{r}^{n-1+r}\textrm{}$)       or
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You should use (r-1)C(n-1). I assumed that children are distinguishable. :)
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Straight forward integer solution problem

$(x_1 +1) + (x_2 +1) + (x_3 +1)=7$

$x_1 + x_2 + x_3 =4$
now do $(n+r-1)C(r-1)$ $where,n=4 , r=3$
$=15$
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actually I got confused as for e.g: Distribute 7 balls to 3 children : so it should be 3^7 rit?
and if the balls are identical x1+x2+x3=7 as then many combinations would be repeating if we use 3^7 am I right