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    20 Choose 8

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

    What is 20 choose 8?

    Answer

    20 choose 8 is
    125,970

    Order doesn't matter, no repeats: 125,970 ways to choose 8 of 20 items.

    C(20, 8) = 20! / (8! · 12!)

    = (20 × 19 × 18 × … × 13) / (8 × 7 × 6 × … × 1)

    8 factors on top and bottom

    = 5,079,110,400 / 40,320

    = 125,970

    If order matters (permutations): P(20, 8) = 20 × 19 × 18 × … × 13 = 5,079,110,400 — each combination in 8! = 40,320 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--8Copy
    <a href="https://calculat.io/en/number/combinations/20--8">20 Choose 8: Combinations C(20, 8) - Calculatio</a>Copy
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    20 Choose 8: Combinations C(20, 8). 20 choose 8 = 125,970: the number of ways to choose 8 of 20 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/20--8/generated.jpgCopy

    n choose 8 for other n

    n choose 8Answer
    8 choose 81
    9 choose 89
    10 choose 845
    11 choose 8165
    12 choose 8495
    13 choose 81,287
    14 choose 83,003
    15 choose 86,435
    16 choose 812,870
    17 choose 824,310
    18 choose 843,758
    19 choose 875,582
    20 choose 8125,970
    Recalculate with different values ↑

    FAQ

    What is 20 choose 8?

    20 choose 8 is 125,970

    Why is 20 choose 8 the same as 20 choose 12?

    Every way to choose 8 of 20 items leaves exactly 12 behind, so choosing 8 and choosing which 12 to leave out are the same count: 20 choose 8 = 20 choose 12 = 125,970. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(20, 8) = 5,079,110,400. Each of the 125,970 combinations can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also