Statistics - Permutation with Replacement


Each of several possible ways in which a set or number of things can be ordered or arranged is called permutation Combination with replacement in probability is selecting an object from an unordered list multiple times.

Permutation with replacement is defined and given by the following probability function:


${^nP_r = n^r }$

Where −

  • ${n}$ = number of items which can be selected.

  • ${r}$ = number of items which are selected.

  • ${^nP_r}$ = Ordered list of items or permutions


Problem Statement:

Electronic device usually require a personal code to operate. This particular device uses 4-digits code. Calculate how many codes are possible.


Each code is represented by r=4 permutation with replacement of set of 10 digits{0,1,2,3,4,5,6,7,8,9}

${^{10}P_4 = (10)^4 \\[7pt] \ = 10000 }$