# With the word Quicker, how many ways can we arrange the letters if U and I can't be together?

##### 1 Answer

1800 ways

#### Explanation:

Let's start off by seeing that there are 7 letters. If the letters were all different and we didn't have placement issues (U and I can't be set together), we could arrange them in

With working with the U, I placement restriction, we can approach it by calculating the number of ways we can place U and I and then multiply by the ways we can place the remaining letters.

**U, I Placement**

One way we can calculate this is to count the number of ways we can place U and I. They can be in places:

**Placing the remainder**

We can now place the remaining letters. There are five of them and if they were all different, we could place them in

**Putting it together**

We multiply the number of ways we can place the U and I with the ways to place the remaining letters: