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    18 Choose 16

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

    What is 18 choose 16?

    Answer

    18 choose 16 is
    153

    Order doesn't matter, no repeats: 153 ways to choose 16 of 18 items.

    Choosing 16 of 18 is the same as leaving 2 out: C(18, 16) = C(18, 2).

    C(18, 16) = 18! / (16! · 2!)

    = C(18, 2)

    = (18 × 17) / (2 × 1)
    = 306 / 2

    = 153

    If order matters (permutations): P(18, 16) = 18 × 17 × 16 × … × 3 = 3,201,186,852,864,000 — each combination in 16! = 20,922,789,888,000 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--16Copy
    <a href="https://calculat.io/en/number/combinations/18--16">18 Choose 16: Combinations C(18, 16) - Calculatio</a>Copy
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    18 Choose 16: Combinations C(18, 16). 18 choose 16 = 153: the number of ways to choose 16 of 18 items when order doesn't matter and nothing repeats. C(18, 16) = (18 × 17) / (2 × 1).
    https://calculat.io/en/number/combinations/18--16/generated.jpgCopy

    n choose 16 for other n

    n choose 16Answer
    16 choose 161
    17 choose 1617
    18 choose 16153
    19 choose 16969
    20 choose 164,845
    Recalculate with different values ↑

    FAQ

    What is 18 choose 16?

    18 choose 16 is 153

    Why is 18 choose 16 the same as 18 choose 2?

    Every way to choose 16 of 18 items leaves exactly 2 behind, so choosing 16 and choosing which 2 to leave out are the same count: 18 choose 16 = 18 choose 2 = 153. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(18, 16) = 3,201,186,852,864,000. Each of the 153 combinations can be put in order in 16! = 20,922,789,888,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also