## eugeniaday Group Title 7!*8!*3!/5!*9! one year ago one year ago

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1. UnkleRhaukus Group Title

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

what is n

3. UnkleRhaukus Group Title

some natural number

so if its not a number how would i solve this

5. Azteck Group Title

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

6. UnkleRhaukus Group Title

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

72576

8. UnkleRhaukus Group Title

$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 Group Title

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 Group Title

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 Group Title

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

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 Group Title

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 Group Title

can you show me your working

19. agent0smith Group Title

@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.