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

F. G. Avkhadiev ; A. N. Chuprunov

Lobachevskii journal of mathematics, Tome 25 (2007), pp. 3-7

Résumé

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 $p\to e^{-\frac{m(m-1)}2\alpha_0}$ as $n,N\to\infty$ such that $\alpha=\frac nN\to\alpha_0\infty$. In the case $2\le q$ we also find an explicit formula for the probability and prove that $p\to1$ as $n,N\to\infty$ such that $\alpha=\frac nN\le\alpha'\infty$.

Détail

Keywords: generating function, Cauchy integral.
Mots-clés : equiprobable scheme for group allocation of particles