Statistics - Permutation with Replacement


Advertisements

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:

Formula

${^nP_r = n^r }$

Where −

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

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

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

Example

Problem Statement:

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

Solution:

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}

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

Useful Video Courses

Video

Class 11th Statistics for Economics

40 Lectures 3.5 hours

Madhu Bhatia

Video

Statistics

40 Lectures 2 hours

Megha Aggarwal

Video

Applied Statistics in Python for Machine Learning Engineers

66 Lectures 1.5 hours

Mike West

Video

An Introduction to Wait Statistics in SQL Server

22 Lectures 1 hours

Mike West

Video

Geospatial Data Science: Statistics and Machine Learning

60 Lectures 12 hours

Michael Miller

Video

Basic Statistics & Regression for Machine Learning in Python

65 Lectures 5 hours

Abhilash Nelson

Advertisements