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    19 Choose 14

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

    What is 19 choose 14?

    Answer

    19 choose 14 is
    11,628

    Order doesn't matter, no repeats: 11,628 ways to choose 14 of 19 items.

    Choosing 14 of 19 is the same as leaving 5 out: C(19, 14) = C(19, 5).

    C(19, 14) = 19! / (14! · 5!)

    = C(19, 5)

    = (19 × 18 × 17 × 16 × 15) / (5 × 4 × 3 × 2 × 1)
    = 1,395,360 / 120

    = 11,628

    If order matters (permutations): P(19, 14) = 19 × 18 × 17 × … × 6 = 1,013,709,170,073,600 — each combination in 14! = 87,178,291,200 orders.

    Row 19 of Pascal's triangle
    k19 choose k
    01
    119
    2171
    3969
    43,876
    511,628
    627,132
    750,388
    875,582
    992,378
    1092,378
    1175,582
    1250,388
    1327,132
    1411,628
    153,876
    16969
    17171
    1819
    191

    Row sum: 219 = 524,288 — all subsets of 19 items.

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    https://calculat.io/en/number/combinations/19--14Copy
    <a href="https://calculat.io/en/number/combinations/19--14">19 Choose 14: Combinations C(19, 14) - Calculatio</a>Copy
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    19 Choose 14: Combinations C(19, 14). 19 choose 14 = 11,628: the number of ways to choose 14 of 19 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/19--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 19 choose 14?

    19 choose 14 is 11,628

    Why is 19 choose 14 the same as 19 choose 5?

    Every way to choose 14 of 19 items leaves exactly 5 behind, so choosing 14 and choosing which 5 to leave out are the same count: 19 choose 14 = 19 choose 5 = 11,628. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(19, 14) = 1,013,709,170,073,600. Each of the 11,628 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