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    19 Choose 13

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

    What is 19 choose 13?

    Answer

    19 choose 13 is
    27,132

    Order doesn't matter, no repeats: 27,132 ways to choose 13 of 19 items.

    Choosing 13 of 19 is the same as leaving 6 out: C(19, 13) = C(19, 6).

    C(19, 13) = 19! / (13! · 6!)

    = C(19, 6)

    = (19 × 18 × 17 × 16 × 15 × 14) / (6 × 5 × 4 × 3 × 2 × 1)
    = 19,535,040 / 720

    = 27,132

    If order matters (permutations): P(19, 13) = 19 × 18 × 17 × … × 7 = 168,951,528,345,600 — each combination in 13! = 6,227,020,800 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--13Copy
    <a href="https://calculat.io/en/number/combinations/19--13">19 Choose 13: Combinations C(19, 13) - Calculatio</a>Copy
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    19 Choose 13: Combinations C(19, 13). 19 choose 13 = 27,132: the number of ways to choose 13 of 19 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/19--13/generated.jpgCopy

    n choose 13 for other n

    n choose 13Answer
    13 choose 131
    14 choose 1314
    15 choose 13105
    16 choose 13560
    17 choose 132,380
    18 choose 138,568
    19 choose 1327,132
    20 choose 1377,520
    Recalculate with different values ↑

    FAQ

    What is 19 choose 13?

    19 choose 13 is 27,132

    Why is 19 choose 13 the same as 19 choose 6?

    Every way to choose 13 of 19 items leaves exactly 6 behind, so choosing 13 and choosing which 6 to leave out are the same count: 19 choose 13 = 19 choose 6 = 27,132. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(19, 13) = 168,951,528,345,600. Each of the 27,132 combinations can be put in order in 13! = 6,227,020,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also