In how many distinct ways can the letters of the word MEDDLE be arranged?

Step-by-step explanation:

If we had 6 unique letters, such as STABLE, we'd be able to arrange the letters in  

6

!

=

720

ways (we'd have 6 choices of what the first letter could be, 5 for the next letter, 4 for the next, etc... giving  

6

×

5

×

4

×

3

×

2

×

1

=

6

!

In our case, we have 2 sets of letters where there are more than 1 - we have two S's and two T's. And so we have to divide out the number of ways each of them can order  

(

S

1

T

A

T

E

S

2

is the same as  

(

S

2

T

A

T

E

S

1

)

and so we'll have:

6

!

2

!

2

!

=

6

×

5

×

4

×

3

×

2

!

2

×

2

!

=

180