Question

How do you write all the permutations of the letters A, B, C and D?

Answer 1

In this question, we need to write all the possible permutations of the letters A, B, C and D. Permutations are nothing but the number of ways of arranging items in a particular order. It’s a mathematical technique. First we can find the total number of ways to arrange the given letters. Then we can write all the possible arrangements of the given letters.
Formula used :
$n! = n\left( n – 1 \right)\left( n – 2 \right)\left( n – 3 \right)\ldots$

Complete step by step answer:
Given, A, B, C and D
The letters A, B, C and D can be arranged in $4!$ Ways.
$4! =4\times 3\times 2\times 1$
On simplifying,
We get,
$4! =24$
Therefore the total possible arrangements of the letters A, B, C and D is $24$ .
Now we can write all the permutations of the given letters.
First we can begin with the letter A and then B, C and D
Thus the permutations of the letters A, B, C and D are
ABCD, ABDC, ACBD, ACDB, ADBC, ADCB,
BACD, BADC, BCAD, BCDA, BDAC, BDCA,
CABD, CADB, CBAD, CBDA, CDAB, CDBA,
DABC, DACB, DBAC, DBCA, DCAB, DCBA

Note:
We should not get confused with combinations and permutations. Permutations is the choice of arranging $r$ things from the set of $n$ things that are also without replacement . In other words, selection and arrangement of subsets is known as permutation whereas the non fraction order of selection is known as combination. Combinations is defined as a way of selecting items from a collection whereas the order of selection does not matter. The rule of the permutation is anything permute itself is equivalent to itself factorial. In combination, the order of the object is not important.