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    17 Choose 1

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

    What is 17 choose 1?

    Answer

    17 choose 1 is
    17

    Order doesn't matter, no repeats: 17 ways to choose 1 of 17 items.

    C(17, 1) = 17! / (1! · 16!)

    = 17 / 1

    = 17

    Row 17 of Pascal's triangle
    k17 choose k
    01
    117
    2136
    3680
    42,380
    56,188
    612,376
    719,448
    824,310
    924,310
    1019,448
    1112,376
    126,188
    132,380
    14680
    15136
    1617
    171

    Row sum: 217 = 131,072 — all subsets of 17 items.

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    https://calculat.io/en/number/combinations/17--1Copy
    <a href="https://calculat.io/en/number/combinations/17--1">17 Choose 1: Combinations C(17, 1) - Calculatio</a>Copy
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    17 Choose 1: Combinations C(17, 1). 17 choose 1 = 17: the number of ways to choose 1 of 17 items when order doesn't matter and nothing repeats. C(17, 1) = 17 / 1.
    https://calculat.io/en/number/combinations/17--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 17 choose 1?

    17 choose 1 is 17

    Why is 17 choose 1 the same as 17 choose 16?

    Every way to choose 1 of 17 items leaves exactly 16 behind, so choosing 1 and choosing which 16 to leave out are the same count: 17 choose 1 = 17 choose 16 = 17. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    The same 17: with 1 chosen item there is only one order, so P(17, 1) = 17 choose 1 = 17. Order starts to matter from 2 items on: n × (n − 1) arrangements.

    See Also