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eugeniaday

  • 2 years ago

7!*8!*3!/5!*9!

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  1. UnkleRhaukus
    • 2 years ago
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    \[n!=n\times(n-1)!\]

  2. eugeniaday
    • 2 years ago
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    what is n

  3. UnkleRhaukus
    • 2 years ago
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    some natural number

  4. eugeniaday
    • 2 years ago
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    so if its not a number how would i solve this

  5. Azteck
    • 2 years ago
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    Well you're diverting yourself to your own question here.

  6. UnkleRhaukus
    • 2 years ago
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    \[\frac{\color{teal}{7!}\times8!\times3!}{5!\times\color{orange}{9!}}=\frac{\color{teal}{7\times6\times5!}\times8!\times3!}{5!\times\color{orange}{9\times8!}}\]

  7. eugeniaday
    • 2 years ago
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    72576

  8. UnkleRhaukus
    • 2 years ago
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    \[n!=n\times(n-1)!\]\[\quad=n\times(n-1)\times(n-2)!\]\[\quad=n\times(n-1)\times(n-2)\times\cdots\times3\times2\times1\]

  9. eugeniaday
    • 2 years ago
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    no still not getting

  10. UnkleRhaukus
    • 2 years ago
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    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
    • 2 years ago
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    the trick is to cancel common factors ,

  12. eugeniaday
    • 2 years ago
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    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
    • 2 years ago
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    \[\frac{{7!}\times8!\times3!}{5!\times{9!}}=\frac{{7\times6\times5!}\times8!\times3!}{5!\times{9\times8!}}=\frac{{7\times6\times\cancel{5!}}\times\cancel{8!}\times3!}{\cancel{5!}\times9\times\cancel{8!}}\]

  14. eugeniaday
    • 2 years ago
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    so 14

  15. eugeniaday
    • 2 years ago
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    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
    • 2 years ago
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    i choose not to fully expand the factorials because it takes to much space and time, bytheway 14 isn't quite right

  17. eugeniaday
    • 2 years ago
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    what its not that was one of the options

  18. UnkleRhaukus
    • 2 years ago
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    can you show me your working

  19. agent0smith
    • 2 years ago
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    @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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