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    18 Choose 1

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

    What is 18 choose 1?

    Answer

    18 choose 1 is
    18

    Order doesn't matter, no repeats: 18 ways to choose 1 of 18 items.

    C(18, 1) = 18! / (1! · 17!)

    = 18 / 1

    = 18

    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--1Copy
    <a href="https://calculat.io/en/number/combinations/18--1">18 Choose 1: Combinations C(18, 1) - Calculatio</a>Copy
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    18 Choose 1: Combinations C(18, 1). 18 choose 1 = 18: the number of ways to choose 1 of 18 items when order doesn't matter and nothing repeats. C(18, 1) = 18 / 1.
    https://calculat.io/en/number/combinations/18--1/generated.jpgCopy

    n choose 1 for other n

    n choose 1Answer
    6 choose 16
    7 choose 17
    8 choose 18
    9 choose 19
    10 choose 110
    11 choose 111
    12 choose 112
    13 choose 113
    14 choose 114
    15 choose 115
    16 choose 116
    17 choose 117
    18 choose 118
    19 choose 119
    20 choose 120
    Recalculate with different values ↑

    FAQ

    What is 18 choose 1?

    18 choose 1 is 18

    Why is 18 choose 1 the same as 18 choose 17?

    Every way to choose 1 of 18 items leaves exactly 17 behind, so choosing 1 and choosing which 17 to leave out are the same count: 18 choose 1 = 18 choose 17 = 18. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    The same 18: with 1 chosen item there is only one order, so P(18, 1) = 18 choose 1 = 18. Order starts to matter from 2 items on: n × (n − 1) arrangements.

    See Also