How do you simplify (21!)/(17!4!)?
2 Answers
Explanation:
(21!)/(17! xx 4!)=(17! xx 18 xx 19 xx 20 xx 21)/(17! xx4!)
may be simplified as
=(18 xx 19 xx 20 xx 21)/(1 xx 2 xx 3 xx 4)
and this may be further simplified as
=(9 xx 19 xx 5 xx 7)/(1 xx 1 xx 1 xx 1)
=9 xx19 xx 5 xx 7
=5985
Oct 30, 2016
Write out the definitions of each factorial and you should get
=> (1cdot2cdot3cdot4cdots17cdot18cdot19cdot20cdot21)/((1cdot2cdot3cdot4cdots15cdot16cdot17)(1cdot2cdot3cdot4))
The portion of
= (18cdot19cdot20cdot21)/(1cdot2cdot3cdot4)
= ((19-1)cdot19cdot20(20+1))/(24)
= ((361 - 19)cdot(400 + 20))/(24)
= (342cdot420)/(24)
= (171cdot420)/(12)
= (171cdot210)/(6)
= (57cdot210)/(2)
= 57cdot105
= 57cdot(100 + 5)
= 5700 + 57cdot10/2
= 5700 + 285
= color(blue)(5985)
