# Thread: How to find the total number of unique three-letter arrangements for this word?

1. ## How to find the total number of unique three-letter arrangements for this word?

How do i determine the total number of unique three-letter arrangements that are possible using the letters in the word "believe"?

2. ## Re: How to find the total number of unique three-letter arrangements for this word?

Originally Posted by thegameplayer
How do i determine the total number of unique three-letter arrangements that are possible using the letters in the word "believe"?
There is one string with all $\displaystyle e^\’s$: $\displaystyle eee$

Look at the collection $\displaystyle \{b,e,l,i,v\}$, how many three letters strings of distinct letters from that set are there?

Look at the collection $\displaystyle \{b,l,i,v\}$, how many three letters strings with one leter from that set with two $\displaystyle e^’s$ are there?