MHB Combination Problem: C(70,67) = 54,740

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How come the combination of C(70,67) is 54,740?
 
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yakin said:
How come the combination of C(70,67) is 54,740?

The combination function is defined as:

$$C(n,r)={n \choose r}\equiv\frac{n!}{r!(n-r)!}$$

And so we have:

$${70 \choose 67}=\frac{70!}{67!(70-67)!}=\frac{70\cdot69\cdot68\cdot67!}{67!\cdot3!}=\frac{70\cdot69\cdot68}{3\cdot2}=35\cdot23\cdot68=54740$$
 

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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