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

2 Answers
Jan 16, 2016

Answer:

#60#

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 #""^5P_3=(5!)/((5-3)!)=60#.

Jan 16, 2016

Answer:

#60#

Explanation:

There are #5# ways to choose the first letter, #4# to choose the next letter and #3# ways to choose the third letter, hence #5xx4xx3 = 60# ways to choose an arrangement of #3# letters from #5#.

In general, if you have #n# distinct objects from which to choose an arrangement of #k# items then the number of ways you can do it is:

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

In our example, #n=5#, #k=3# and:

#""^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 #k# items from #n# is:

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