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    18 Choose 13

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

    What is 18 choose 13?

    Answer

    18 choose 13 is
    8,568

    Order doesn't matter, no repeats: 8,568 ways to choose 13 of 18 items.

    Choosing 13 of 18 is the same as leaving 5 out: C(18, 13) = C(18, 5).

    C(18, 13) = 18! / (13! · 5!)

    = C(18, 5)

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

    = 8,568

    If order matters (permutations): P(18, 13) = 18 × 17 × 16 × … × 6 = 53,353,114,214,400 — each combination in 13! = 6,227,020,800 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--13Copy
    <a href="https://calculat.io/en/number/combinations/18--13">18 Choose 13: Combinations C(18, 13) - Calculatio</a>Copy
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    18 Choose 13: Combinations C(18, 13). 18 choose 13 = 8,568: the number of ways to choose 13 of 18 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/18--13/generated.jpgCopy

    n choose 13 for other n

    n choose 13Answer
    13 choose 131
    14 choose 1314
    15 choose 13105
    16 choose 13560
    17 choose 132,380
    18 choose 138,568
    19 choose 1327,132
    20 choose 1377,520
    Recalculate with different values ↑

    FAQ

    What is 18 choose 13?

    18 choose 13 is 8,568

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

    Every way to choose 13 of 18 items leaves exactly 5 behind, so choosing 13 and choosing which 5 to leave out are the same count: 18 choose 13 = 18 choose 5 = 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, 13) = 53,353,114,214,400. Each of the 8,568 combinations can be put in order in 13! = 6,227,020,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also