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

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The combination C(70,67) equals 54,740 because it calculates the number of ways to choose 67 items from a set of 70. The formula used is C(n,r) = n! / (r!(n-r)!), which simplifies for this case to C(70,67) = 70! / (67! * 3!). By canceling out the factorials, the calculation reduces to (70 * 69 * 68) / 6. The final result confirms that C(70,67) indeed equals 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:

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

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