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    20 Choose 6

    Combination Calculator
    Total items (n)
    Items chosen (k)

    What is 20 choose 6?

    Answer

    20 choose 6 is
    38,760

    Order doesn't matter, no repeats: 38,760 ways to choose 6 of 20 items.

    C(20, 6) = 20! / (6! · 14!)

    = (20 × 19 × 18 × 17 × 16 × 15) / (6 × 5 × 4 × 3 × 2 × 1)
    = 27,907,200 / 720

    = 38,760

    If order matters (permutations): P(20, 6) = 20 × 19 × 18 × 17 × 16 × 15 = 27,907,200 — each combination in 6! = 720 orders.

    Row 20 of Pascal's triangle
    k20 choose k
    01
    120
    2190
    31,140
    44,845
    515,504
    638,760
    777,520
    8125,970
    9167,960
    10184,756
    11167,960
    12125,970
    1377,520
    1438,760
    1515,504
    164,845
    171,140
    18190
    1920
    201

    Row sum: 220 = 1,048,576 — all subsets of 20 items.

    See Also

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    https://calculat.io/en/number/combinations/20--6Copy
    <a href="https://calculat.io/en/number/combinations/20--6">20 Choose 6: Combinations C(20, 6) - Calculatio</a>Copy
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    20 Choose 6: Combinations C(20, 6). 20 choose 6 = 38,760: the number of ways to choose 6 of 20 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/20--6/generated.jpgCopy

    n choose 6 for other n

    n choose 6Answer
    6 choose 61
    7 choose 67
    8 choose 628
    9 choose 684
    10 choose 6210
    11 choose 6462
    12 choose 6924
    13 choose 61,716
    14 choose 63,003
    15 choose 65,005
    16 choose 68,008
    17 choose 612,376
    18 choose 618,564
    19 choose 627,132
    20 choose 638,760
    Recalculate with different values ↑

    FAQ

    What is 20 choose 6?

    20 choose 6 is 38,760

    Why is 20 choose 6 the same as 20 choose 14?

    Every way to choose 6 of 20 items leaves exactly 14 behind, so choosing 6 and choosing which 14 to leave out are the same count: 20 choose 6 = 20 choose 14 = 38,760. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(20, 6) = 27,907,200. Each of the 38,760 combinations can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also