If `n` biscuits are distributed among `N` beggars, find the chance that a particular beggar will get `r(<n)` biscuits.

Question

If n biscuits are distributed among N beggars, find the chance that a particular beggar will get r(A.((N-1)^(n-r))/(N^(n))B.(.^(n)C_(r ))/(N^(n-r))C.(.^(n)C_(r )(N-1)^(r ))/(N^(n))D.(.^(n)C_(r )(N-1)^(n-r))/(N^(n))` Select the correct answer from above options

Answer 1

Correct Answer - D 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=Nn n-times Now, r biscuits can be given to a particular beggar in .nCr 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 .nCr×(N-1)n-r Hence, required probability = .nCr×(N-1)n-r Nn