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    20 Choose 12

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

    What is 20 choose 12?

    Answer

    20 choose 12 is
    125,970

    Order doesn't matter, no repeats: 125,970 ways to choose 12 of 20 items.

    Choosing 12 of 20 is the same as leaving 8 out: C(20, 12) = C(20, 8).

    C(20, 12) = 20! / (12! · 8!)

    = C(20, 8)

    = (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, 12) = 20 × 19 × 18 × … × 9 = 60,339,831,552,000 — each combination in 12! = 479,001,600 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.

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    https://calculat.io/en/number/combinations/20--12Copy
    <a href="https://calculat.io/en/number/combinations/20--12">20 Choose 12: Combinations C(20, 12) - Calculatio</a>Copy
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    20 Choose 12: Combinations C(20, 12). 20 choose 12 = 125,970: the number of ways to choose 12 of 20 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/20--12/generated.jpgCopy

    n choose 12 for other n

    n choose 12Answer
    12 choose 121
    13 choose 1213
    14 choose 1291
    15 choose 12455
    16 choose 121,820
    17 choose 126,188
    18 choose 1218,564
    19 choose 1250,388
    20 choose 12125,970
    Recalculate with different values ↑

    FAQ

    What is 20 choose 12?

    20 choose 12 is 125,970

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

    Every way to choose 12 of 20 items leaves exactly 8 behind, so choosing 12 and choosing which 8 to leave out are the same count: 20 choose 12 = 20 choose 8 = 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, 12) = 60,339,831,552,000. Each of the 125,970 combinations can be put in order in 12! = 479,001,600 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also