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    20 Choose 14

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

    What is 20 choose 14?

    Answer

    20 choose 14 is
    38,760

    Order doesn't matter, no repeats: 38,760 ways to choose 14 of 20 items.

    Choosing 14 of 20 is the same as leaving 6 out: C(20, 14) = C(20, 6).

    C(20, 14) = 20! / (14! · 6!)

    = C(20, 6)

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

    = 38,760

    If order matters (permutations): P(20, 14) = 20 × 19 × 18 × … × 7 = 3,379,030,566,912,000 — each combination in 14! = 87,178,291,200 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--14Copy
    <a href="https://calculat.io/en/number/combinations/20--14">20 Choose 14: Combinations C(20, 14) - Calculatio</a>Copy
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    20 Choose 14: Combinations C(20, 14). 20 choose 14 = 38,760: the number of ways to choose 14 of 20 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/20--14/generated.jpgCopy

    n choose 14 for other n

    n choose 14Answer
    14 choose 141
    15 choose 1415
    16 choose 14120
    17 choose 14680
    18 choose 143,060
    19 choose 1411,628
    20 choose 1438,760
    Recalculate with different values ↑

    FAQ

    What is 20 choose 14?

    20 choose 14 is 38,760

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

    Every way to choose 14 of 20 items leaves exactly 6 behind, so choosing 14 and choosing which 6 to leave out are the same count: 20 choose 14 = 20 choose 6 = 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, 14) = 3,379,030,566,912,000. Each of the 38,760 combinations can be put in order in 14! = 87,178,291,200 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also