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    11 Choose 11

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

    What is 11 choose 11?

    Answer

    11 choose 11 is
    1

    Order doesn't matter, no repeats: 1 way to choose 11 of 11 items.

    There is exactly one way: take all.

    C(11, 11) = 11! / (11! · 0!)

    = 1

    0! = 1 (an empty product), so 11! cancels out completely.

    If order matters (permutations): P(11, 11) = 11 × 10 × 9 × … × 1 = 39,916,800 — each combination in 11! = 39,916,800 orders.

    Row 11 of Pascal's triangle
    k11 choose k
    01
    111
    255
    3165
    4330
    5462
    6462
    7330
    8165
    955
    1011
    111

    Row sum: 211 = 2,048 — all subsets of 11 items.

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    https://calculat.io/en/number/combinations/11--11Copy
    <a href="https://calculat.io/en/number/combinations/11--11">11 Choose 11: Combinations C(11, 11) - Calculatio</a>Copy
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    11 Choose 11: Combinations C(11, 11). 11 choose 11 = 1: the number of ways to choose 11 of 11 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/11--11/generated.jpgCopy

    n choose 11 for other n

    n choose 11Answer
    11 choose 111
    12 choose 1112
    13 choose 1178
    14 choose 11364
    15 choose 111,365
    16 choose 114,368
    17 choose 1112,376
    18 choose 1131,824
    19 choose 1175,582
    20 choose 11167,960
    Recalculate with different values ↑

    FAQ

    What is 11 choose 11?

    11 choose 11 is 1

    Why is 11 choose 11 the same as 11 choose 0?

    Every way to choose 11 of 11 items leaves exactly 0 behind, so choosing 11 and choosing which 0 to leave out are the same count: 11 choose 11 = 11 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(11, 11) = 39,916,800. The only combination — all 11 items — can be put in order in 11! = 39,916,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also