Question

In how many ways can you rearrange the letters A, B, C, D, E?

Answer 1

Hint: We will use the concept of permutations to solve this question. We will define the term permutation. Then we will make slots which are equal to the number of given letters. Then we will count the possibilities to fill in each of these slots. The total number of ways the five slots can be filled is the same as the number of ways to rearrange the given five letters.

Complete step by step answer:
A permutation is defined as a reordering or rearrangement of the elements of a given set. We are given five letters. Let us consider five slots for placing these letters.
Now, to fill the first slot, we can choose any one of the 5 letters. So, there are 5 ways of filling the first slot. Next is the second slot. For this, we have to choose from among the four remaining letters after filling the first slot. So, there are 4 ways to fill in the second slot. We are now left with 3 letters. So, to fill in the third slot we have 3 ways. After that, we can fill in the fourth slot from the remaining two letters in 2 ways. And for the last slot, we have only 1 way. So, the total number of ways to fill in these five slots is $5!$, that is, $5\times 4\times 3\times 2\times 1=120$.

The total number of ways to fill the five slots is equal to the total number of rearrangements of the given five letters. Therefore, the answer is 120 ways.

Note: It is important to know the concept of permutations and combinations. We should know the difference between these two. When we are concerned with order, we look for permutations.. And when the order of elements does not matter, we use combinations. The principle of counting is the key aspect in these concepts.