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anonymous

  • one year ago

Evaluate the given binomial coefficient (109/3)

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  1. anonymous
    • one year ago
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    \[\binom{109}{3}\]?

  2. anonymous
    • one year ago
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    I have no idea how to do these problems.

  3. anonymous
    • one year ago
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    Yes, that is it.

  4. anonymous
    • one year ago
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    \[\frac{109\times 108\times 107}{3\times 2}\]

  5. anonymous
    • one year ago
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    else cheat http://www.wolframalpha.com/input/?i=109+choose+3

  6. anonymous
    • one year ago
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    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?

  7. anonymous
    • one year ago
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    yes that is the result

  8. anonymous
    • one year ago
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    \[\binom{109}{3}=\frac{\overbrace{109\times 108\times 107}^{\text {three terms}}}{3!}\]

  9. anonymous
    • one year ago
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    So we know to go back three numbers (109, 108, 107) because it's over 3?

  10. anonymous
    • one year ago
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    Why do we multiply 3 by 2?

  11. anonymous
    • one year ago
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    the denominator is \(3!=3\times 2\)

  12. anonymous
    • one year ago
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    as another example \[\binom{10}{4}=\frac{10\times 9\times 8\times 7}{4\times 3\times 2}\]

  13. anonymous
    • one year ago
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    If the problem were, for instance (50/7), would it be (50x49x48x47x46x45x44/7x6x5x4x3x2)?

  14. anonymous
    • one year ago
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    yes

  15. anonymous
    • one year ago
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    it is a whole number in each case, so to compute, cancel first multiply last

  16. anonymous
    • one year ago
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    And (7/7) would be (7x6x5x4x3x2x1/7x6x5x4x3x2)? Basically I just want to confirm that the denominator just always counts down to 2?

  17. anonymous
    • one year ago
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    \(\binom{n}{n}=1\)

  18. anonymous
    • one year ago
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    yes, some people write a 1 there too, but that is silly because multiplying by one is like doing nothing

  19. anonymous
    • one year ago
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    like they might write \(4!=4\times 3\times 2\times1\)

  20. anonymous
    • one year ago
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    Gotcha. So the "denominator" will always count down to 2, and the "numerator" will count down the number of the denominator?

  21. anonymous
    • one year ago
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    doesn't count town to the number in the bottom counts down that many terms (like in the example you wrote)

  22. anonymous
    • one year ago
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    yeah i guess what you said is right if i interpret it correctly there is also a formula, but i wouldn't use it

  23. anonymous
    • one year ago
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    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!

  24. anonymous
    • one year ago
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    yw

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