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    9 Choose 9

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

    What is 9 choose 9?

    Answer

    9 choose 9 is
    1

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

    There is exactly one way: take all.

    C(9, 9) = 9! / (9! · 0!)

    = 1

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

    If order matters (permutations): P(9, 9) = 9 × 8 × 7 × … × 1 = 362,880 — each combination in 9! = 362,880 orders.

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

    n choose 9 for other n

    n choose 9Answer
    9 choose 91
    10 choose 910
    11 choose 955
    12 choose 9220
    13 choose 9715
    14 choose 92,002
    15 choose 95,005
    16 choose 911,440
    17 choose 924,310
    18 choose 948,620
    19 choose 992,378
    20 choose 9167,960
    Recalculate with different values ↑

    FAQ

    What is 9 choose 9?

    9 choose 9 is 1

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

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

    How many ways are there if order matters?

    P(9, 9) = 362,880. The only combination — all 9 items — can be put in order in 9! = 362,880 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also