# How many three letter arrangements can be formed if a letter is used only once? [TIGER]

##### 2 Answers

#### Explanation:

This is equivalent to asking in how many different ways can u select 3 from an available 5 and arrange them.

This is then the permutation

#### Explanation:

There are *arrangement* of

In general, if you have *arrangement* of

#""^nP_k = (n!)/((n-k)!)#

In our example,

#""^5P_3 = (5!)/((5-3)!) = (5!)/(2!) = (5xx4xx3xxcolor(red)(cancel(color(black)(2)))xxcolor(red)(cancel(color(black)(1))))/(color(red)(cancel(color(black)(2)))xxcolor(red)(cancel(color(black)(1)))) = 5xx4xx3=60#

If the order of the chosen items does not matter, then the number of ways to choose

#""^nC_k = ((n),(k)) = (n!)/(k!(n-k)!)#