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    19 Choose 18

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

    What is 19 choose 18?

    Answer

    19 choose 18 is
    19

    Order doesn't matter, no repeats: 19 ways to choose 18 of 19 items.

    Choosing 18 of 19 is the same as leaving 1 out: C(19, 18) = C(19, 1).

    C(19, 18) = 19! / (18! · 1!)

    = C(19, 1)

    = 19 / 1

    = 19

    If order matters (permutations): P(19, 18) = 19 × 18 × 17 × … × 2 = 121,645,100,408,832,000 — each combination in 18! = 6,402,373,705,728,000 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--18Copy
    <a href="https://calculat.io/en/number/combinations/19--18">19 Choose 18: Combinations C(19, 18) - Calculatio</a>Copy
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    19 Choose 18: Combinations C(19, 18). 19 choose 18 = 19: the number of ways to choose 18 of 19 items when order doesn't matter and nothing repeats. C(19, 18) = 19 / 1.
    https://calculat.io/en/number/combinations/19--18/generated.jpgCopy

    n choose 18 for other n

    n choose 18Answer
    18 choose 181
    19 choose 1819
    20 choose 18190
    Recalculate with different values ↑

    FAQ

    What is 19 choose 18?

    19 choose 18 is 19

    Why is 19 choose 18 the same as 19 choose 1?

    Every way to choose 18 of 19 items leaves exactly 1 behind, so choosing 18 and choosing which one to leave out are the same count: 19 choose 18 = 19 choose 1 = 19. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(19, 18) = 121,645,100,408,832,000. Each of the 19 combinations can be put in order in 18! = 6,402,373,705,728,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also