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    16 Choose 16

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

    What is 16 choose 16?

    Answer

    16 choose 16 is
    1

    Order doesn't matter, no repeats: 1 way to choose 16 of 16 items.

    There is exactly one way: take all.

    C(16, 16) = 16! / (16! · 0!)

    = 1

    0! = 1 (an empty product), so 16! cancels out completely.

    If order matters (permutations): P(16, 16) = 16 × 15 × 14 × … × 1 = 20,922,789,888,000 — each combination in 16! = 20,922,789,888,000 orders.

    Row 16 of Pascal's triangle
    k16 choose k
    01
    116
    2120
    3560
    41,820
    54,368
    68,008
    711,440
    812,870
    911,440
    108,008
    114,368
    121,820
    13560
    14120
    1516
    161

    Row sum: 216 = 65,536 — all subsets of 16 items.

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    https://calculat.io/en/number/combinations/16--16Copy
    <a href="https://calculat.io/en/number/combinations/16--16">16 Choose 16: Combinations C(16, 16) - Calculatio</a>Copy
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    16 Choose 16: Combinations C(16, 16). 16 choose 16 = 1: the number of ways to choose 16 of 16 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/16--16/generated.jpgCopy

    n choose 16 for other n

    n choose 16Answer
    16 choose 161
    17 choose 1617
    18 choose 16153
    19 choose 16969
    20 choose 164,845
    Recalculate with different values ↑

    FAQ

    What is 16 choose 16?

    16 choose 16 is 1

    Why is 16 choose 16 the same as 16 choose 0?

    Every way to choose 16 of 16 items leaves exactly 0 behind, so choosing 16 and choosing which 0 to leave out are the same count: 16 choose 16 = 16 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(16, 16) = 20,922,789,888,000. The only combination — all 16 items — can be put in order in 16! = 20,922,789,888,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also