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

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