How do you simplify #(20!)/(17!)#?

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Answer 1 · 2018-04-30T01:34:39

Given: #(20!)/(17!)#

Substitute #20! =17!(18)(19)(20)#

#(20!)/(17!) = (17!(18)(19)(20))/(17!)#

Cancel the two factorials:

#(20!)/(17!) = (18)(19)(20)#

Multiply the 3 numbers:

#(20!)/(17!) = 6840#

Answer 2 · 2018-06-24T20:27:18

#6840#

Let's just expand this out:

#(20*19*18*17...)/(17!)#

We notice that the continuation of #20!# starting with #17# cancels with the denominator of #17!#.

#(20*19*18*cancel(17...))/cancel(17!)#

This leaves us with

#20*19*18#

#=>360*19=6840#

Hope this helps!