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

1 Answer
MathFact-orials.blogspot.com
Mar 17, 2017

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:

#5040/24#

and the other is by breaking down the multiplication:

#(7xx6xx5xx4!)/(4!)#

Either way, we arrive at 210

Related questions
See all questions in Combinations and Permutations
Impact of this question
5330 views around the world
You can reuse this answer
Creative Commons License