If n biscuits are distributed among N beggars, the probability that a particular beggar will get r(<n) biscuits, is

$\frac{^nC_r(N-1)^{n-r}}{N^n}$

Since a biscuit can be given to any one of N beggars. Therefore, each biscuit can be distributed in N ways. So, the total number of ways of distributing n biscuits among N beggars is

$N ×N×...×N=N^n $

n-times

Now, r biscuits can be given to a particular beggar in ${^nC_r}$, ways and the remaining (n-r) biscuits can be distributed to (N-1) beggars in $(N-1)^{n-r}$ ways. Thus, the number of ways in which a particular beggar receives r biscuits is

${^nC}_r  × (N-1)^{n-r}$

Hence, required probability $= \frac{^nC_r(N-1)^{n-r}}{N^n}$