# Thread: letters

1. ## letters

how many arrangements of the letters SWARMED are possible if A and R must be separated by at least 1 letter.

im night sure if this is a combinations or permutations question.

this is what i did. i found the total combinations if A and R are together which is 5!. A and R can be A and R or R and A so thats 2! so 5!*2! than total ways of arranging the letters are 7! so 7!- 5!*2! is the answer i get. i dont think this is right.

2. ## Re: letters

Originally Posted by markosheehan
how many arrangements of the letters SWARMED are possible if A and R must be separated by at least 1 letter.
The way you want to count these is correct, but your count is off.
Look at $\boxed{AR},S,W,M,E,D$. There are $6!$ ways to arrange those six items (not 5!).
So why $7!-2\cdot 6!~???$

3. ## Re: letters

sorry yes 6. 3600 is the right answer.

do you know when you use permutations vs combinations ? whats the difference

4. ## Re: letters

Same as:
1234567
12 or 21 nowhere to be seen!

lowest: 1324567
highest: 7654231

5. ## Re: letters

Originally Posted by markosheehan
do you know when you use permutations vs combinations ? whats the difference
Permutations are about order while combinations are about content.

For example, suppose the is a collection of people: a club, a school class, any group.

If the question asks 'how many ways can four members be selected to plan a party' then we use combinations.
That is strictly about the content of the committee.

On the other hand, if we ask 'how many can we select a Pres., VP, Treasurer & Secretary' then we use permutations.
We are still selecting four people, but in this case order makes a difference.