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1. UnkleRhaukus

$n!=n\times(n-1)!$

what is n

3. UnkleRhaukus

some natural number

so if its not a number how would i solve this

5. Azteck

Well you're diverting yourself to your own question here.

6. UnkleRhaukus

$\frac{\color{teal}{7!}\times8!\times3!}{5!\times\color{orange}{9!}}=\frac{\color{teal}{7\times6\times5!}\times8!\times3!}{5!\times\color{orange}{9\times8!}}$

72576

8. 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$

no still not getting

10. UnkleRhaukus

for example $4!=4\times3\times2\times1$$6!=6\times5\times4\times3\times2\times1$ $\frac{4!}{6!}=\frac{4\times3\times2\times1}{6\times5\times4\times3\times2\times1}=\frac{4!}{6\times5\times4!}=\frac1{6\times5}=\frac1{30}$

11. UnkleRhaukus

the trick is to cancel common factors ,

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

13. UnkleRhaukus

$\frac{{7!}\times8!\times3!}{5!\times{9!}}=\frac{{7\times6\times5!}\times8!\times3!}{5!\times{9\times8!}}=\frac{{7\times6\times\cancel{5!}}\times\cancel{8!}\times3!}{\cancel{5!}\times9\times\cancel{8!}}$

so 14

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

16. UnkleRhaukus

i choose not to fully expand the factorials because it takes to much space and time, bytheway 14 isn't quite right

what its not that was one of the options

18. UnkleRhaukus

can you show me your working

19. 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.