Evaluate the given binomial coefficient (109/3)

- anonymous

Evaluate the given binomial coefficient (109/3)

- jamiebookeater

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- anonymous

\[\binom{109}{3}\]?

- anonymous

I have no idea how to do these problems.

- anonymous

Yes, that is it.

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## More answers

- anonymous

\[\frac{109\times 108\times 107}{3\times 2}\]

- anonymous

else cheat
http://www.wolframalpha.com/input/?i=109+choose+3

- anonymous

How does one know which steps to follow to do this problem. Just to confirm, the answer would be the resulting number of that fraction?

- anonymous

yes that is the result

- anonymous

\[\binom{109}{3}=\frac{\overbrace{109\times 108\times 107}^{\text {three terms}}}{3!}\]

- anonymous

So we know to go back three numbers (109, 108, 107) because it's over 3?

- anonymous

Why do we multiply 3 by 2?

- anonymous

the denominator is \(3!=3\times 2\)

- anonymous

as another example \[\binom{10}{4}=\frac{10\times 9\times 8\times 7}{4\times 3\times 2}\]

- anonymous

If the problem were, for instance (50/7), would it be (50x49x48x47x46x45x44/7x6x5x4x3x2)?

- anonymous

yes

- anonymous

it is a whole number in each case, so to compute, cancel first multiply last

- anonymous

And (7/7) would be (7x6x5x4x3x2x1/7x6x5x4x3x2)? Basically I just want to confirm that the denominator just always counts down to 2?

- anonymous

\(\binom{n}{n}=1\)

- anonymous

yes, some people write a 1 there too, but that is silly because multiplying by one is like doing nothing

- anonymous

like they might write \(4!=4\times 3\times 2\times1\)

- anonymous

Gotcha. So the "denominator" will always count down to 2, and the "numerator" will count down the number of the denominator?

- anonymous

doesn't count town to the number in the bottom
counts down that many terms (like in the example you wrote)

- anonymous

yeah i guess what you said is right if i interpret it correctly
there is also a formula, but i wouldn't use it

- anonymous

Yeah that's what I meant (the number of terms, not all the way down to that number). Thank you very much for explaining this all so clearly!

- anonymous

yw

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