ncr, n=120, r=3?

3 Answers

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  • 4 weeks ago

    I'm going to write this as:

    C(n,r) 

    You want to calculate C(120,3)

    When doing this by hand, just start by writing the numbers as a fraction:

    120

    -----

    3

    Then multiply by the next smaller number on top and bottom. Stop when you get to 1 on the bottom:

    120 × 119 × 118

    ----------------------

    .. 3 . × . 2 . × . 1

    Now cancel every number in the denominator using common factors. In this case, you can cancel 3 and 2 against a 6 in 120.

    20 x 119 x 118

    -------------------

    . 1. ×. 1 . × 1

    When you have canceled everything in the denominator down to ones, multiply the remaining numbers in the numerator:

    20 × 119 × 118

    Answer:

    280,840

    P.S. To double-check your answer, you can just type "120 choose 3" into Google. Or you can type "C(120,3)" into WolframAlpha.

  • 120! / (3! * (120 - 3)!) =>

    120 * 119 * 118 * 117! / (6 * 117!) =>

    120 * 119 * 118 / 6 =>

    20 * 119 * 118 =>

    20 * (120 - 1) * (120 - 2) =>

    20 * (14400 - 240 - 120 + 2) =>

    20 * (14400 - 360 + 2) =>

    20 * (14042) =>

    280840

  • 4 weeks ago

    (120 • 119 • 118) ÷ (3 • 2 • 1)

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