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    18 Choose 5

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

    What is 18 choose 5?

    Answer

    18 choose 5 is
    8,568

    Order doesn't matter, no repeats: 8,568 ways to choose 5 of 18 items.

    C(18, 5) = 18! / (5! · 13!)

    = (18 × 17 × 16 × 15 × 14) / (5 × 4 × 3 × 2 × 1)
    = 1,028,160 / 120

    = 8,568

    If order matters (permutations): P(18, 5) = 18 × 17 × 16 × 15 × 14 = 1,028,160 — each combination in 5! = 120 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.

    See Also

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    https://calculat.io/en/number/combinations/18--5Copy
    <a href="https://calculat.io/en/number/combinations/18--5">18 Choose 5: Combinations C(18, 5) - Calculatio</a>Copy
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    18 Choose 5: Combinations C(18, 5). 18 choose 5 = 8,568: the number of ways to choose 5 of 18 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/18--5/generated.jpgCopy

    n choose 5 for other n

    n choose 5Answer
    6 choose 56
    7 choose 521
    8 choose 556
    9 choose 5126
    10 choose 5252
    11 choose 5462
    12 choose 5792
    13 choose 51,287
    14 choose 52,002
    15 choose 53,003
    16 choose 54,368
    17 choose 56,188
    18 choose 58,568
    19 choose 511,628
    20 choose 515,504
    Recalculate with different values ↑

    FAQ

    What is 18 choose 5?

    18 choose 5 is 8,568

    Why is 18 choose 5 the same as 18 choose 13?

    Every way to choose 5 of 18 items leaves exactly 13 behind, so choosing 5 and choosing which 13 to leave out are the same count: 18 choose 5 = 18 choose 13 = 8,568. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(18, 5) = 1,028,160. Each of the 8,568 combinations can be put in order in 5! = 120 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also