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    19 Choose 5

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

    What is 19 choose 5?

    Answer

    19 choose 5 is
    11,628

    Order doesn't matter, no repeats: 11,628 ways to choose 5 of 19 items.

    C(19, 5) = 19! / (5! · 14!)

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

    = 11,628

    If order matters (permutations): P(19, 5) = 19 × 18 × 17 × 16 × 15 = 1,395,360 — each combination in 5! = 120 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.

    See Also

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    https://calculat.io/en/number/combinations/19--5Copy
    <a href="https://calculat.io/en/number/combinations/19--5">19 Choose 5: Combinations C(19, 5) - Calculatio</a>Copy
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    19 Choose 5: Combinations C(19, 5). 19 choose 5 = 11,628: the number of ways to choose 5 of 19 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/19--5/generated.jpgCopy

    n choose 5 for other n

    n choose 5Answer
    6 choose 56
    7 choose 521
    8 choose 556
    9 choose 5126
    10 choose 5252
    11 choose 5462
    12 choose 5792
    13 choose 51,287
    14 choose 52,002
    15 choose 53,003
    16 choose 54,368
    17 choose 56,188
    18 choose 58,568
    19 choose 511,628
    20 choose 515,504
    Recalculate with different values ↑

    FAQ

    What is 19 choose 5?

    19 choose 5 is 11,628

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

    Every way to choose 5 of 19 items leaves exactly 14 behind, so choosing 5 and choosing which 14 to leave out are the same count: 19 choose 5 = 19 choose 14 = 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, 5) = 1,395,360. Each of the 11,628 combinations can be put in order in 5! = 120 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also