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    9 Choose 0

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

    What is 9 choose 0?

    Answer

    9 choose 0 is
    1

    Order doesn't matter, no repeats: 1 way to choose 0 of 9 items.

    There is exactly one way: take none.

    C(9, 0) = 9! / (0! · 9!)

    = 1

    0! = 1 (an empty product), so 9! cancels out completely.

    Row 9 of Pascal's triangle
    k9 choose k
    01
    19
    236
    384
    4126
    5126
    684
    736
    89
    91

    Row sum: 29 = 512 — all subsets of 9 items.

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    https://calculat.io/en/number/combinations/9--0Copy
    <a href="https://calculat.io/en/number/combinations/9--0">9 Choose 0: Combinations C(9, 0) - Calculatio</a>Copy
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    9 Choose 0: Combinations C(9, 0). 9 choose 0 = 1: the number of ways to choose 0 of 9 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/9--0/generated.jpgCopy

    n choose 0 for other n

    n choose 0Answer
    2 choose 01
    3 choose 01
    4 choose 01
    5 choose 01
    6 choose 01
    7 choose 01
    8 choose 01
    9 choose 01
    10 choose 01
    11 choose 01
    12 choose 01
    13 choose 01
    14 choose 01
    15 choose 01
    16 choose 01
    Recalculate with different values ↑

    FAQ

    What is 9 choose 0?

    9 choose 0 is 1

    Why is 9 choose 0 the same as 9 choose 9?

    Every way to choose 0 of 9 items leaves exactly 9 behind, so choosing 0 and choosing which 9 to leave out are the same count: 9 choose 0 = 9 choose 9 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    The same 1: with 0 chosen items there is only one order, so P(9, 0) = 9 choose 0 = 1. Order starts to matter from 2 items on: n × (n − 1) arrangements.

    See Also