Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    18 Choose 14

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

    What is 18 choose 14?

    Answer

    18 choose 14 is
    3,060

    Order doesn't matter, no repeats: 3,060 ways to choose 14 of 18 items.

    Choosing 14 of 18 is the same as leaving 4 out: C(18, 14) = C(18, 4).

    C(18, 14) = 18! / (14! · 4!)

    = C(18, 4)

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

    = 3,060

    If order matters (permutations): P(18, 14) = 18 × 17 × 16 × … × 5 = 266,765,571,072,000 — each combination in 14! = 87,178,291,200 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

    Share This Calculation
    Print
    https://calculat.io/en/number/combinations/18--14Copy
    <a href="https://calculat.io/en/number/combinations/18--14">18 Choose 14: Combinations C(18, 14) - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    18 Choose 14: Combinations C(18, 14). 18 choose 14 = 3,060: the number of ways to choose 14 of 18 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/18--14/generated.jpgCopy

    n choose 14 for other n

    n choose 14Answer
    14 choose 141
    15 choose 1415
    16 choose 14120
    17 choose 14680
    18 choose 143,060
    19 choose 1411,628
    20 choose 1438,760
    Recalculate with different values ↑

    FAQ

    What is 18 choose 14?

    18 choose 14 is 3,060

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

    Every way to choose 14 of 18 items leaves exactly 4 behind, so choosing 14 and choosing which 4 to leave out are the same count: 18 choose 14 = 18 choose 4 = 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, 14) = 266,765,571,072,000. Each of the 3,060 combinations can be put in order in 14! = 87,178,291,200 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also