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    19 Choose 4

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

    What is 19 choose 4?

    Answer

    19 choose 4 is
    3,876

    Order doesn't matter, no repeats: 3,876 ways to choose 4 of 19 items.

    C(19, 4) = 19! / (4! · 15!)

    = (19 × 18 × 17 × 16) / (4 × 3 × 2 × 1)
    = 93,024 / 24

    = 3,876

    If order matters (permutations): P(19, 4) = 19 × 18 × 17 × 16 = 93,024 — each combination in 4! = 24 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--4Copy
    <a href="https://calculat.io/en/number/combinations/19--4">19 Choose 4: Combinations C(19, 4) - Calculatio</a>Copy
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    19 Choose 4: Combinations C(19, 4). 19 choose 4 = 3,876: the number of ways to choose 4 of 19 items when order doesn't matter and nothing repeats. C(19, 4) = (19 × 18 × 17 × 16) / (4 × 3 × 2 × 1).
    https://calculat.io/en/number/combinations/19--4/generated.jpgCopy

    n choose 4 for other n

    n choose 4Answer
    7 choose 435
    8 choose 470
    9 choose 4126
    10 choose 4210
    11 choose 4330
    12 choose 4495
    13 choose 4715
    14 choose 41,001
    15 choose 41,365
    16 choose 41,820
    17 choose 42,380
    18 choose 43,060
    19 choose 43,876
    20 choose 44,845
    24 choose 410,626
    Recalculate with different values ↑

    FAQ

    What is 19 choose 4?

    19 choose 4 is 3,876

    Why is 19 choose 4 the same as 19 choose 15?

    Every way to choose 4 of 19 items leaves exactly 15 behind, so choosing 4 and choosing which 15 to leave out are the same count: 19 choose 4 = 19 choose 15 = 3,876. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(19, 4) = 93,024. Each of the 3,876 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also