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    8 Choose 8

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

    What is 8 choose 8?

    Answer

    8 choose 8 is
    1

    Order doesn't matter, no repeats: 1 way to choose 8 of 8 items.

    There is exactly one way: take all.

    C(8, 8) = 8! / (8! · 0!)

    = 1

    0! = 1 (an empty product), so 8! cancels out completely.

    If order matters (permutations): P(8, 8) = 8 × 7 × 6 × … × 1 = 40,320 — each combination in 8! = 40,320 orders.

    Row 8 of Pascal's triangle
    k8 choose k
    01
    18
    228
    356
    470
    556
    628
    78
    81

    Row sum: 28 = 256 — all subsets of 8 items.

    See Also

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    https://calculat.io/en/number/combinations/8--8Copy
    <a href="https://calculat.io/en/number/combinations/8--8">8 Choose 8: Combinations C(8, 8) - Calculatio</a>Copy
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    8 Choose 8: Combinations C(8, 8). 8 choose 8 = 1: the number of ways to choose 8 of 8 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/8--8/generated.jpgCopy

    n choose 8 for other n

    n choose 8Answer
    8 choose 81
    9 choose 89
    10 choose 845
    11 choose 8165
    12 choose 8495
    13 choose 81,287
    14 choose 83,003
    15 choose 86,435
    16 choose 812,870
    17 choose 824,310
    18 choose 843,758
    19 choose 875,582
    20 choose 8125,970
    Recalculate with different values ↑

    FAQ

    What is 8 choose 8?

    8 choose 8 is 1

    Why is 8 choose 8 the same as 8 choose 0?

    Every way to choose 8 of 8 items leaves exactly 0 behind, so choosing 8 and choosing which 0 to leave out are the same count: 8 choose 8 = 8 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(8, 8) = 40,320. The only combination — all 8 items — can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also