Question

How many words can be formed by using the W,X,Y,Z if repetitions is not allowed?

Answer 1

Answer:

24

Step-by-step explanation:

What you have here is a permutation, seeing as each element can only be used once.

We have 4 letters initially, so we can choose any 1 as our first letter. We have 4 choices for our first letter

However, once we choose our first letter, we can't use it anymore, so, for our second letter, we can only choose from the remaining 3 letters.

Furthermore, once we choose our second letter, we can only choose our 3rd letter from the remaining two letters we didn't choose yet.

Finally, our last letter will always be the one we didn't choose the last 3 times. So there is only one choice here.

Going off of this, we have four choices for the 1st letter, three choices for the 2nd letter, two choices for the 3rd letter, and one choice for the 4th letter

The way to calculate how many permutations we have without repetition is using factorials

N!

Where N is the number of elements you have.

In this case, it would be 4!

4! is 4 * 3 * 2 * 1

Which equals 24

If you notice, each number in 4! is the number of options we have for each choice. 4, then 3, and so on