Question

How many different arrangements can be made with the letters in the word ZEBRA?

Answer 1

`5! =120`

Explanation:

The word ZEBRA has 5 letters.

So when considering the different arrangements, we have five choices for the first letter, four for the second, three for the third, etc.

So

#"Total no. of arrangements " = 5xx4xx3xx2xx1=5! =120#

Answer 2

`120` arrangements

Explanation:

We can approach this types of problems in this way:

For this there are five spaces to fill the letters `{z,e,b,r,a}`

We can say you can place one of these letters in the first spaces, there are 5 possibilities for first space

Then there are 4 possibilities to fill the second space, as one has already been used for the first space

Then there are 3 possibilities to fill the the third

and so on...

We just multiples together:

`color(blue)(5xx4xx3xx2xx1 = 120 " arrangements "`

In general, if we have `n` different characters

There will be `nxx(n-1)xx(n-2)xx ... xx 3xx2xx1` arrangements

This is also know as `n! = nxx(n-1)xx(n-2)xx ... xx 3xx2xx1`

So if we wanted to find the numbers of arrangements for ABCDEFGHI

There are 9 different letters, hence `9!` arrangements

`=> 362880`