Chapter 9.6, Problem 47E

To determine

To write: all permutations of the letters $A,B,C$ , and $D$ .

Explanation of Solution

Calculation:

If a set of $n$ elements has $n_1$ of one kind of object, $n_2$ of 2^nd object…and so on with

  $n=n_1+n_2+\mathrm{...}+n_k$

Then number of distinguishable permutations of the $n$ objects is given by

  $\frac{n!}{n_1!\cdot n_2!\cdot \cdot \cdot \cdot \cdot n_k!}$

Let us consider the following letters

A, B, C, D

There will be ${}_4{P}_4$ permutations because we want to arrange 4 letters in 4 positions.

All the permutations are mentioned as below,

ABCD

ABDC

ACBD

ACDB

ADBC

ADCB

BACD

BADC

BCAD

BCDA

BDCA

CABD

CADB

CBAD

CBDA

CDAB

CDBA

DABC

DACB

DBAC

DCAB

DCBA