How do you evaluate #(19!)/( 13!)#?

1 Answer
smendyka
Jun 25, 2017

See a solution process below:

Explanation:

First,

#n! = 1 * 2 * 3 * ... * n#

Where #n# in a positive integer.

Therefore:

#19! = 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * ... * 1#

#13! = 13 * 12 * 11 * 10 * ... * 1#

#(19!)/(13!) = (19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * ... * 1)/(13 * 12 * 11 * 10 * ... * 1)#

#(19!)/(13!) = (19 * 18 * 17 * 16 * 15 * 14 * color(red)(cancel(color(black)(13))) * color(blue)(cancel(color(black)(12))) * color(green)(cancel(color(black)(11))) * color(purple)(cancel(color(black)(10))) cancel( * ... * ))/(color(red)(cancel(color(black)(13))) * color(blue)(cancel(color(black)(12))) * color(green)(cancel(color(black)(11))) * color(purple)(cancel(color(black)(10))) cancel( * ... * ))#

#(19!)/(13!) = 19 * 18 * 17 * 16 * 15 * 14#

#(19!)/(13!) = 19,535,040#

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