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    16 Choose 1

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

    What is 16 choose 1?

    Answer

    16 choose 1 is
    16

    Order doesn't matter, no repeats: 16 ways to choose 1 of 16 items.

    C(16, 1) = 16! / (1! · 15!)

    = 16 / 1

    = 16

    Row 16 of Pascal's triangle
    k16 choose k
    01
    116
    2120
    3560
    41,820
    54,368
    68,008
    711,440
    812,870
    911,440
    108,008
    114,368
    121,820
    13560
    14120
    1516
    161

    Row sum: 216 = 65,536 — all subsets of 16 items.

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    https://calculat.io/en/number/combinations/16--1Copy
    <a href="https://calculat.io/en/number/combinations/16--1">16 Choose 1: Combinations C(16, 1) - Calculatio</a>Copy
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    16 Choose 1: Combinations C(16, 1). 16 choose 1 = 16: the number of ways to choose 1 of 16 items when order doesn't matter and nothing repeats. C(16, 1) = 16 / 1.
    https://calculat.io/en/number/combinations/16--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 16 choose 1?

    16 choose 1 is 16

    Why is 16 choose 1 the same as 16 choose 15?

    Every way to choose 1 of 16 items leaves exactly 15 behind, so choosing 1 and choosing which 15 to leave out are the same count: 16 choose 1 = 16 choose 15 = 16. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    The same 16: with 1 chosen item there is only one order, so P(16, 1) = 16 choose 1 = 16. Order starts to matter from 2 items on: n × (n − 1) arrangements.

    See Also