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    18 Choose 6

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

    What is 18 choose 6?

    Answer

    18 choose 6 is
    18,564

    Order doesn't matter, no repeats: 18,564 ways to choose 6 of 18 items.

    C(18, 6) = 18! / (6! · 12!)

    = (18 × 17 × 16 × 15 × 14 × 13) / (6 × 5 × 4 × 3 × 2 × 1)
    = 13,366,080 / 720

    = 18,564

    If order matters (permutations): P(18, 6) = 18 × 17 × 16 × 15 × 14 × 13 = 13,366,080 — each combination in 6! = 720 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--6Copy
    <a href="https://calculat.io/en/number/combinations/18--6">18 Choose 6: Combinations C(18, 6) - Calculatio</a>Copy
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    18 Choose 6: Combinations C(18, 6). 18 choose 6 = 18,564: the number of ways to choose 6 of 18 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/18--6/generated.jpgCopy

    n choose 6 for other n

    n choose 6Answer
    6 choose 61
    7 choose 67
    8 choose 628
    9 choose 684
    10 choose 6210
    11 choose 6462
    12 choose 6924
    13 choose 61,716
    14 choose 63,003
    15 choose 65,005
    16 choose 68,008
    17 choose 612,376
    18 choose 618,564
    19 choose 627,132
    20 choose 638,760
    Recalculate with different values ↑

    FAQ

    What is 18 choose 6?

    18 choose 6 is 18,564

    Why is 18 choose 6 the same as 18 choose 12?

    Every way to choose 6 of 18 items leaves exactly 12 behind, so choosing 6 and choosing which 12 to leave out are the same count: 18 choose 6 = 18 choose 12 = 18,564. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(18, 6) = 13,366,080. Each of the 18,564 combinations can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also