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    12 Choose 11

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

    What is 12 choose 11?

    Answer

    12 choose 11 is
    12

    Order doesn't matter, no repeats: 12 ways to choose 11 of 12 items.

    Choosing 11 of 12 is the same as leaving 1 out: C(12, 11) = C(12, 1).

    C(12, 11) = 12! / (11! · 1!)

    = C(12, 1)

    = 12 / 1

    = 12

    If order matters (permutations): P(12, 11) = 12 × 11 × 10 × … × 2 = 479,001,600 — each combination in 11! = 39,916,800 orders.

    Row 12 of Pascal's triangle
    k12 choose k
    01
    112
    266
    3220
    4495
    5792
    6924
    7792
    8495
    9220
    1066
    1112
    121

    Row sum: 212 = 4,096 — all subsets of 12 items.

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    https://calculat.io/en/number/combinations/12--11Copy
    <a href="https://calculat.io/en/number/combinations/12--11">12 Choose 11: Combinations C(12, 11) - Calculatio</a>Copy
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    12 Choose 11: Combinations C(12, 11). 12 choose 11 = 12: the number of ways to choose 11 of 12 items when order doesn't matter and nothing repeats. C(12, 11) = 12 / 1.
    https://calculat.io/en/number/combinations/12--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 12 choose 11?

    12 choose 11 is 12

    Why is 12 choose 11 the same as 12 choose 1?

    Every way to choose 11 of 12 items leaves exactly 1 behind, so choosing 11 and choosing which one to leave out are the same count: 12 choose 11 = 12 choose 1 = 12. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(12, 11) = 479,001,600. Each of the 12 combinations can be put in order in 11! = 39,916,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also