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 15

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

    What is 19 choose 15?

    Answer

    19 choose 15 is
    3,876

    Order doesn't matter, no repeats: 3,876 ways to choose 15 of 19 items.

    Choosing 15 of 19 is the same as leaving 4 out: C(19, 15) = C(19, 4).

    C(19, 15) = 19! / (15! · 4!)

    = C(19, 4)

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

    = 3,876

    If order matters (permutations): P(19, 15) = 19 × 18 × 17 × … × 5 = 5,068,545,850,368,000 — each combination in 15! = 1,307,674,368,000 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--15Copy
    <a href="https://calculat.io/en/number/combinations/19--15">19 Choose 15: Combinations C(19, 15) - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    19 Choose 15: Combinations C(19, 15). 19 choose 15 = 3,876: the number of ways to choose 15 of 19 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/19--15/generated.jpgCopy

    n choose 15 for other n

    n choose 15Answer
    15 choose 151
    16 choose 1516
    17 choose 15136
    18 choose 15816
    19 choose 153,876
    20 choose 1515,504
    Recalculate with different values ↑

    FAQ

    What is 19 choose 15?

    19 choose 15 is 3,876

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

    Every way to choose 15 of 19 items leaves exactly 4 behind, so choosing 15 and choosing which 4 to leave out are the same count: 19 choose 15 = 19 choose 4 = 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, 15) = 5,068,545,850,368,000. Each of the 3,876 combinations can be put in order in 15! = 1,307,674,368,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also