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I'm having issues working out the answer to a question $C(6,2)$. I'm working it out wrong because I've got this

$$C(6,2) = \frac{6!}{2(6-2)!} = \frac{6!}{2\ 4!} = \frac{6!}{8!} = \frac{720}{40320} = 0.0178.$$

Michael Albanese
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user2956865
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  • You want $6!/(2!4!)$. Note that $2!4!$ is not $8!$. – André Nicolas Nov 18 '13 at 03:58
  • yeah sorry I just worked it out its 6!/ 2(4)! so you do the 4 first which is 24 then multiply it by 2 so you should get 720/48 which is 15 – user2956865 Nov 18 '13 at 03:59
  • Yes, it is correct. It is simpler, and worth knowing, to do it like this. Note that $6!=(6)(5)(4!)$. The $41$ cancels the $4!$ at the bottom, so you end up with $\frac{(6)(5)}{2}=15$. This shortcut can be important when you are dealing with a much bigger thing, like $\frac{100!}{2!98!}$. If you do it like I just showed, you quickly get $4950$. – André Nicolas Nov 18 '13 at 04:42

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$${6\choose 2}={6!\over 2!(6-2)!}={6!\over 2!4!}={6\cdot5\cdot4!\over 4!2!}={6\cdot5\over 2!}={30\over 2}=15$$

1233dfv
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