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    20 Choose 1

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

    What is 20 choose 1?

    Answer

    20 choose 1 is
    20

    Order doesn't matter, no repeats: 20 ways to choose 1 of 20 items.

    C(20, 1) = 20! / (1! · 19!)

    = 20 / 1

    = 20

    Row 20 of Pascal's triangle
    k20 choose k
    01
    120
    2190
    31,140
    44,845
    515,504
    638,760
    777,520
    8125,970
    9167,960
    10184,756
    11167,960
    12125,970
    1377,520
    1438,760
    1515,504
    164,845
    171,140
    18190
    1920
    201

    Row sum: 220 = 1,048,576 — all subsets of 20 items.

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    https://calculat.io/en/number/combinations/20--1Copy
    <a href="https://calculat.io/en/number/combinations/20--1">20 Choose 1: Combinations C(20, 1) - Calculatio</a>Copy
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    20 Choose 1: Combinations C(20, 1). 20 choose 1 = 20: the number of ways to choose 1 of 20 items when order doesn't matter and nothing repeats. C(20, 1) = 20 / 1.
    https://calculat.io/en/number/combinations/20--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 20 choose 1?

    20 choose 1 is 20

    Why is 20 choose 1 the same as 20 choose 19?

    Every way to choose 1 of 20 items leaves exactly 19 behind, so choosing 1 and choosing which 19 to leave out are the same count: 20 choose 1 = 20 choose 19 = 20. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    The same 20: with 1 chosen item there is only one order, so P(20, 1) = 20 choose 1 = 20. Order starts to matter from 2 items on: n × (n − 1) arrangements.

    See Also