anonymous
  • anonymous
7!*8!*3!/5!*9!
Mathematics
jamiebookeater
  • jamiebookeater
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UnkleRhaukus
  • UnkleRhaukus
\[n!=n\times(n-1)!\]
anonymous
  • anonymous
what is n
UnkleRhaukus
  • UnkleRhaukus
some natural number

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anonymous
  • anonymous
so if its not a number how would i solve this
anonymous
  • anonymous
Well you're diverting yourself to your own question here.
UnkleRhaukus
  • UnkleRhaukus
\[\frac{\color{teal}{7!}\times8!\times3!}{5!\times\color{orange}{9!}}=\frac{\color{teal}{7\times6\times5!}\times8!\times3!}{5!\times\color{orange}{9\times8!}}\]
anonymous
  • anonymous
72576
UnkleRhaukus
  • UnkleRhaukus
\[n!=n\times(n-1)!\]\[\quad=n\times(n-1)\times(n-2)!\]\[\quad=n\times(n-1)\times(n-2)\times\cdots\times3\times2\times1\]
anonymous
  • anonymous
no still not getting
UnkleRhaukus
  • UnkleRhaukus
for example \[4!=4\times3\times2\times1\]\[6!=6\times5\times4\times3\times2\times1\] \[\frac{4!}{6!}=\frac{4\times3\times2\times1}{6\times5\times4\times3\times2\times1}=\frac{4!}{6\times5\times4!}=\frac1{6\times5}=\frac1{30}\]
UnkleRhaukus
  • UnkleRhaukus
the trick is to cancel common factors ,
anonymous
  • anonymous
i subtract the 7 and 3 on the top so i would have 8*6*5*4*2*1/8*7*6*4*3*2*1
UnkleRhaukus
  • UnkleRhaukus
\[\frac{{7!}\times8!\times3!}{5!\times{9!}}=\frac{{7\times6\times5!}\times8!\times3!}{5!\times{9\times8!}}=\frac{{7\times6\times\cancel{5!}}\times\cancel{8!}\times3!}{\cancel{5!}\times9\times\cancel{8!}}\]
anonymous
  • anonymous
so 14
anonymous
  • anonymous
but why didnt you right it out all the way as in 7*6*5*4*3*2*1 for all the numbers on top and bottom then facter them out
UnkleRhaukus
  • UnkleRhaukus
i choose not to fully expand the factorials because it takes to much space and time, bytheway 14 isn't quite right
anonymous
  • anonymous
what its not that was one of the options
UnkleRhaukus
  • UnkleRhaukus
can you show me your working
agent0smith
  • agent0smith
@eugeniaday if you do these on your calculator, make sure you use parentheses! 7!*8!*3!/5!*9! is NOT the same as 7!*8!*3!/(5!*9!), and your calculator can't instinctively know what you *meant* to enter.

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