Question

Evaluate the given binomial coefficient (109/3)

Answer 1

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

Answer 2

I have no idea how to do these problems.

Answer 3

Yes, that is it.

Answer 4

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

Answer 5

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

Answer 6

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?

Answer 7

yes that is the result

Answer 8

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

Answer 9

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

Answer 10

Why do we multiply 3 by 2?

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

yes

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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!

Answer 24

yw