What is the value of #4P4#?

1 Answer
Alan P.
Apr 12, 2017

#""_4P_4=color(green)(24)#

Explanation:

#""_4P_4# means the number of ways (permutations) of arranging #4# items from a collection of #4# items.

There are #4# choices for the first item,

and for each of these, there are #3# remaining choices for the second item (or #4xx3=12# choices for selecting and aarranging the first #2# items),

and for each of these, there are #2# remaining choices for the third item (or #4xx3x2=24# choices for selecting and arranging the first #3# items);

and for the fourth item, there is only #1# item left; giving #4xx3xx2xx1=24# choices for selecting and arranging the #4# items).

As a formula
#color(white)("XXX")""_nP_k=(n!)/((n-k)!)#

So (remembering that #0! =1# by definition)
#color(white)("XXX")""_4P_4=(4!)/(0!) = (4xx3xx2xx1)/(0!) =24#

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