Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    19 Choose 6

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

    What is 19 choose 6?

    Answer

    19 choose 6 is
    27,132

    Order doesn't matter, no repeats: 27,132 ways to choose 6 of 19 items.

    C(19, 6) = 19! / (6! · 13!)

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

    = 27,132

    If order matters (permutations): P(19, 6) = 19 × 18 × 17 × 16 × 15 × 14 = 19,535,040 — each combination in 6! = 720 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

    Share This Calculation
    Print
    https://calculat.io/en/number/combinations/19--6Copy
    <a href="https://calculat.io/en/number/combinations/19--6">19 Choose 6: Combinations C(19, 6) - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    19 Choose 6: Combinations C(19, 6). 19 choose 6 = 27,132: the number of ways to choose 6 of 19 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/19--6/generated.jpgCopy

    n choose 6 for other n

    n choose 6Answer
    6 choose 61
    7 choose 67
    8 choose 628
    9 choose 684
    10 choose 6210
    11 choose 6462
    12 choose 6924
    13 choose 61,716
    14 choose 63,003
    15 choose 65,005
    16 choose 68,008
    17 choose 612,376
    18 choose 618,564
    19 choose 627,132
    20 choose 638,760
    Recalculate with different values ↑

    FAQ

    What is 19 choose 6?

    19 choose 6 is 27,132

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

    Every way to choose 6 of 19 items leaves exactly 13 behind, so choosing 6 and choosing which 13 to leave out are the same count: 19 choose 6 = 19 choose 13 = 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, 6) = 19,535,040. Each of the 27,132 combinations can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also