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    5 Choose 1

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

    What is 5 choose 1?

    Answer

    5 choose 1 is
    5

    Order doesn't matter, no repeats: 5 ways to choose 1 of 5 items.

    C(5, 1) = 5! / (1! · 4!)

    = 5 / 1

    = 5

    Row 5 of Pascal's triangle
    k5 choose k
    01
    15
    210
    310
    45
    51

    Row sum: 25 = 32 — all subsets of 5 items.

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    https://calculat.io/en/number/combinations/5--1Copy
    <a href="https://calculat.io/en/number/combinations/5--1">5 Choose 1: Combinations C(5, 1) - Calculatio</a>Copy
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    5 Choose 1: Combinations C(5, 1). 5 choose 1 = 5: the number of ways to choose 1 of 5 items when order doesn't matter and nothing repeats. C(5, 1) = 5 / 1.
    https://calculat.io/en/number/combinations/5--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 5 choose 1?

    5 choose 1 is 5

    Why is 5 choose 1 the same as 5 choose 4?

    Every way to choose 1 of 5 items leaves exactly 4 behind, so choosing 1 and choosing which 4 to leave out are the same count: 5 choose 1 = 5 choose 4 = 5. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    The same 5: with 1 chosen item there is only one order, so P(5, 1) = 5 choose 1 = 5. Order starts to matter from 2 items on: n × (n − 1) arrangements.

    See Also