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    18 Choose 4

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

    What is 18 choose 4?

    Answer

    18 choose 4 is
    3,060

    Order doesn't matter, no repeats: 3,060 ways to choose 4 of 18 items.

    C(18, 4) = 18! / (4! · 14!)

    = (18 × 17 × 16 × 15) / (4 × 3 × 2 × 1)
    = 73,440 / 24

    = 3,060

    If order matters (permutations): P(18, 4) = 18 × 17 × 16 × 15 = 73,440 — each combination in 4! = 24 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--4Copy
    <a href="https://calculat.io/en/number/combinations/18--4">18 Choose 4: Combinations C(18, 4) - Calculatio</a>Copy
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    18 Choose 4: Combinations C(18, 4). 18 choose 4 = 3,060: the number of ways to choose 4 of 18 items when order doesn't matter and nothing repeats. C(18, 4) = (18 × 17 × 16 × 15) / (4 × 3 × 2 × 1).
    https://calculat.io/en/number/combinations/18--4/generated.jpgCopy

    n choose 4 for other n

    n choose 4Answer
    7 choose 435
    8 choose 470
    9 choose 4126
    10 choose 4210
    11 choose 4330
    12 choose 4495
    13 choose 4715
    14 choose 41,001
    15 choose 41,365
    16 choose 41,820
    17 choose 42,380
    18 choose 43,060
    19 choose 43,876
    20 choose 44,845
    24 choose 410,626
    Recalculate with different values ↑

    FAQ

    What is 18 choose 4?

    18 choose 4 is 3,060

    Why is 18 choose 4 the same as 18 choose 14?

    Every way to choose 4 of 18 items leaves exactly 14 behind, so choosing 4 and choosing which 14 to leave out are the same count: 18 choose 4 = 18 choose 14 = 3,060. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(18, 4) = 73,440. Each of the 3,060 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also