## Avkhadiev Farit Gabidinovich

Chuprunov Alexej Nikolaevich

# The probability of a successful allocation of ball groups by boxes

## (*Lobachevskii Journal of Mathematics, Vol.25, pp.3-7* )

Let *p=p*_{Nn} be the probability of a successful allocation of
*n* groups of distinguishable balls in *N* boxes
in equiprobable scheme for group allocation of balls with the following
assumption: each group contains *m* balls
and each box contains not more than
*q* balls from a same group.
If *q=1*, then we easily calculate *p* and observe that *p→
e*^{-α0(m-1)/2} as *n, N→∞* such that
*α = n/N → α*_{0}<∞. In the case *2 ≤ q* we
also find an explicit formula for the probability and prove that
*p→ 1* as *n, N→∞* such that
*α=n/N ≤ α'<∞*.

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