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    18 Choose 15

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

    What is 18 choose 15?

    Answer

    18 choose 15 is
    816

    Order doesn't matter, no repeats: 816 ways to choose 15 of 18 items.

    Choosing 15 of 18 is the same as leaving 3 out: C(18, 15) = C(18, 3).

    C(18, 15) = 18! / (15! · 3!)

    = C(18, 3)

    = (18 × 17 × 16) / (3 × 2 × 1)
    = 4,896 / 6

    = 816

    If order matters (permutations): P(18, 15) = 18 × 17 × 16 × … × 4 = 1,067,062,284,288,000 — each combination in 15! = 1,307,674,368,000 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--15Copy
    <a href="https://calculat.io/en/number/combinations/18--15">18 Choose 15: Combinations C(18, 15) - Calculatio</a>Copy
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    18 Choose 15: Combinations C(18, 15). 18 choose 15 = 816: the number of ways to choose 15 of 18 items when order doesn't matter and nothing repeats. C(18, 15) = (18 × 17 × 16) / (3 × 2 × 1).
    https://calculat.io/en/number/combinations/18--15/generated.jpgCopy

    n choose 15 for other n

    n choose 15Answer
    15 choose 151
    16 choose 1516
    17 choose 15136
    18 choose 15816
    19 choose 153,876
    20 choose 1515,504
    Recalculate with different values ↑

    FAQ

    What is 18 choose 15?

    18 choose 15 is 816

    Why is 18 choose 15 the same as 18 choose 3?

    Every way to choose 15 of 18 items leaves exactly 3 behind, so choosing 15 and choosing which 3 to leave out are the same count: 18 choose 15 = 18 choose 3 = 816. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(18, 15) = 1,067,062,284,288,000. Each of the 816 combinations can be put in order in 15! = 1,307,674,368,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also