How do you simplify #(24!)/(22)#?

1 Answer
George C.
Nov 29, 2015

#(24!)/(22!) = 24xx23 = 552#

#(24!)/22 = 552*21! = 28202200078783610880000#

Explanation:

#24! = 24 xx 23 xx 22 xx 21 xx 20 xx...xx 3 xx 2 xx 1#

So

#(24!)/(22!) = (24 xx 23 xx color(red)(cancel(color(black)(22 xx 21 xx 20 xx...xx 3 xx 2 xx 1))))/color(red)(cancel(color(black)(22 xx 21 xx 20 xx...xx 3 xx 2 xx 1)))#

#=24 xx 23 = 552#

#(24!)/22 = (24 xx 23 xx color(red)(cancel(color(black)(22))) xx 21 xx 20 xx...xx 3 xx 2 xx 1) / color(red)(cancel(color(black)(22)))#

#=24 xx 23 xx 21! = 552*21!#

#=552 * 51090942171709440000#

#=28202200078783610880000#

Related questions
See all questions in Factorial Identities
Impact of this question
3247 views around the world
You can reuse this answer
Creative Commons License