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    19 Choose 17

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

    What is 19 choose 17?

    Answer

    19 choose 17 is
    171

    Order doesn't matter, no repeats: 171 ways to choose 17 of 19 items.

    Choosing 17 of 19 is the same as leaving 2 out: C(19, 17) = C(19, 2).

    C(19, 17) = 19! / (17! · 2!)

    = C(19, 2)

    = (19 × 18) / (2 × 1)
    = 342 / 2

    = 171

    If order matters (permutations): P(19, 17) = 19 × 18 × 17 × … × 3 = 60,822,550,204,416,000 — each combination in 17! = 355,687,428,096,000 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--17Copy
    <a href="https://calculat.io/en/number/combinations/19--17">19 Choose 17: Combinations C(19, 17) - Calculatio</a>Copy
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    19 Choose 17: Combinations C(19, 17). 19 choose 17 = 171: the number of ways to choose 17 of 19 items when order doesn't matter and nothing repeats. C(19, 17) = (19 × 18) / (2 × 1).
    https://calculat.io/en/number/combinations/19--17/generated.jpgCopy

    n choose 17 for other n

    n choose 17Answer
    17 choose 171
    18 choose 1718
    19 choose 17171
    20 choose 171,140
    Recalculate with different values ↑

    FAQ

    What is 19 choose 17?

    19 choose 17 is 171

    Why is 19 choose 17 the same as 19 choose 2?

    Every way to choose 17 of 19 items leaves exactly 2 behind, so choosing 17 and choosing which 2 to leave out are the same count: 19 choose 17 = 19 choose 2 = 171. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(19, 17) = 60,822,550,204,416,000. Each of the 171 combinations can be put in order in 17! = 355,687,428,096,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also