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    3 Choose 1

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

    What is 3 choose 1?

    Answer

    3 choose 1 is
    3

    Order doesn't matter, no repeats: 3 ways to choose 1 of 3 items.

    C(3, 1) = 3! / (1! · 2!)

    = 3 / 1

    = 3

    Row 3 of Pascal's triangle
    k3 choose k
    01
    13
    23
    31

    Row sum: 23 = 8 — all subsets of 3 items.

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    https://calculat.io/en/number/combinations/3--1Copy
    <a href="https://calculat.io/en/number/combinations/3--1">3 Choose 1: Combinations C(3, 1) - Calculatio</a>Copy
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    3 Choose 1: Combinations C(3, 1). 3 choose 1 = 3: the number of ways to choose 1 of 3 items when order doesn't matter and nothing repeats. C(3, 1) = 3 / 1.
    https://calculat.io/en/number/combinations/3--1/generated.jpgCopy

    n choose 1 for other n

    n choose 1Answer
    1 choose 11
    2 choose 12
    3 choose 13
    4 choose 14
    5 choose 15
    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
    Recalculate with different values ↑

    FAQ

    What is 3 choose 1?

    3 choose 1 is 3

    Why is 3 choose 1 the same as 3 choose 2?

    Every way to choose 1 of 3 items leaves exactly 2 behind, so choosing 1 and choosing which 2 to leave out are the same count: 3 choose 1 = 3 choose 2 = 3. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    The same 3: with 1 chosen item there is only one order, so P(3, 1) = 3 choose 1 = 3. Order starts to matter from 2 items on: n × (n − 1) arrangements.

    See Also