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    19 Choose 3

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

    What is 19 choose 3?

    Answer

    19 choose 3 is
    969

    Order doesn't matter, no repeats: 969 ways to choose 3 of 19 items.

    C(19, 3) = 19! / (3! · 16!)

    = (19 × 18 × 17) / (3 × 2 × 1)
    = 5,814 / 6

    = 969

    If order matters (permutations): P(19, 3) = 19 × 18 × 17 = 5,814 — each combination in 3! = 6 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--3Copy
    <a href="https://calculat.io/en/number/combinations/19--3">19 Choose 3: Combinations C(19, 3) - Calculatio</a>Copy
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    19 Choose 3: Combinations C(19, 3). 19 choose 3 = 969: the number of ways to choose 3 of 19 items when order doesn't matter and nothing repeats. C(19, 3) = (19 × 18 × 17) / (3 × 2 × 1).
    https://calculat.io/en/number/combinations/19--3/generated.jpgCopy

    n choose 3 for other n

    n choose 3Answer
    9 choose 384
    10 choose 3120
    11 choose 3165
    12 choose 3220
    13 choose 3286
    14 choose 3364
    15 choose 3455
    16 choose 3560
    17 choose 3680
    18 choose 3816
    19 choose 3969
    20 choose 31,140
    25 choose 32,300
    40 choose 39,880
    100 choose 3161,700
    Recalculate with different values ↑

    FAQ

    What is 19 choose 3?

    19 choose 3 is 969

    Why is 19 choose 3 the same as 19 choose 16?

    Every way to choose 3 of 19 items leaves exactly 16 behind, so choosing 3 and choosing which 16 to leave out are the same count: 19 choose 3 = 19 choose 16 = 969. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(19, 3) = 5,814. Each of the 969 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also