Permutation with Repetition and Replacement

The number of orderings of n objects taken r at a time, with

repetition, is given by

P=n^r

Where:

P is the total number of permutations

n is the total number of objects in the set

r is the total number of choosing objects in the set

Sample Problems:

1. How many (5-letter) ordered codes can be formed with the

letters of the set (A, B, C & D) if we allow to use repeated use of

the same letter?

Given:

P =?; n =4; r =5

Formula: 

P=n^r

Solution:

P= n^r

P= (4)⁵ =4*4*4*4*4 (no need to write)

P= 1024 ordered codes

2. A standard deck of cards has 52 different cards. How many 2-card ordered arrangements can be made by selecting 2 cards with replacement?

Given: 

P =?; n =52; r =2

Formula: 

P=n^r

Solution:

P=n^r

P= (52)² = 52*52

P= 2704 ordered arrangements