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    19 Choose 16

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

    What is 19 choose 16?

    Answer

    19 choose 16 is
    969

    Order doesn't matter, no repeats: 969 ways to choose 16 of 19 items.

    Choosing 16 of 19 is the same as leaving 3 out: C(19, 16) = C(19, 3).

    C(19, 16) = 19! / (16! · 3!)

    = C(19, 3)

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

    = 969

    If order matters (permutations): P(19, 16) = 19 × 18 × 17 × … × 4 = 20,274,183,401,472,000 — each combination in 16! = 20,922,789,888,000 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.

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    https://calculat.io/en/number/combinations/19--16Copy
    <a href="https://calculat.io/en/number/combinations/19--16">19 Choose 16: Combinations C(19, 16) - Calculatio</a>Copy
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    19 Choose 16: Combinations C(19, 16). 19 choose 16 = 969: the number of ways to choose 16 of 19 items when order doesn't matter and nothing repeats. C(19, 16) = (19 × 18 × 17) / (3 × 2 × 1).
    https://calculat.io/en/number/combinations/19--16/generated.jpgCopy

    n choose 16 for other n

    n choose 16Answer
    16 choose 161
    17 choose 1617
    18 choose 16153
    19 choose 16969
    20 choose 164,845
    Recalculate with different values ↑

    FAQ

    What is 19 choose 16?

    19 choose 16 is 969

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

    Every way to choose 16 of 19 items leaves exactly 3 behind, so choosing 16 and choosing which 3 to leave out are the same count: 19 choose 16 = 19 choose 3 = 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, 16) = 20,274,183,401,472,000. Each of the 969 combinations can be put in order in 16! = 20,922,789,888,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also