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    18 Choose 18

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

    What is 18 choose 18?

    Answer

    18 choose 18 is
    1

    Order doesn't matter, no repeats: 1 way to choose 18 of 18 items.

    There is exactly one way: take all.

    C(18, 18) = 18! / (18! · 0!)

    = 1

    0! = 1 (an empty product), so 18! cancels out completely.

    If order matters (permutations): P(18, 18) = 18 × 17 × 16 × … × 1 = 6,402,373,705,728,000 — each combination in 18! = 6,402,373,705,728,000 orders.

    Row 18 of Pascal's triangle
    k18 choose k
    01
    118
    2153
    3816
    43,060
    58,568
    618,564
    731,824
    843,758
    948,620
    1043,758
    1131,824
    1218,564
    138,568
    143,060
    15816
    16153
    1718
    181

    Row sum: 218 = 262,144 — all subsets of 18 items.

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

    18 choose 18 is 1

    Why is 18 choose 18 the same as 18 choose 0?

    Every way to choose 18 of 18 items leaves exactly 0 behind, so choosing 18 and choosing which 0 to leave out are the same count: 18 choose 18 = 18 choose 0 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(18, 18) = 6,402,373,705,728,000. The only combination — all 18 items — 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