How many three-letter sequences can be made from the letters in the word FORESAW?

210

Explanation:

We have 7 letters and we're going to grab 3 at a time to make a word. The order that we pick the 3 letters is important - WAS is different than SAW. And so we use the permutation calculation, the general formula is:

P_(n,k)=(n!)/((n-k)!); n="population", k="picks"

P_(7,3)=(7!)/((7-3)!)=(7!)/(4!)

We can evaluate in a couple of different ways - one is by using a factorial table:

$\frac{5040}{24}$

and the other is by breaking down the multiplication:

(7xx6xx5xx4!)/(4!)

Either way, we arrive at 210