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    13 Choose 11

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

    What is 13 choose 11?

    Answer

    13 choose 11 is
    78

    Order doesn't matter, no repeats: 78 ways to choose 11 of 13 items.

    Choosing 11 of 13 is the same as leaving 2 out: C(13, 11) = C(13, 2).

    C(13, 11) = 13! / (11! · 2!)

    = C(13, 2)

    = (13 × 12) / (2 × 1)
    = 156 / 2

    = 78

    If order matters (permutations): P(13, 11) = 13 × 12 × 11 × … × 3 = 3,113,510,400 — each combination in 11! = 39,916,800 orders.

    Row 13 of Pascal's triangle
    k13 choose k
    01
    113
    278
    3286
    4715
    51,287
    61,716
    71,716
    81,287
    9715
    10286
    1178
    1213
    131

    Row sum: 213 = 8,192 — all subsets of 13 items.

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    https://calculat.io/en/number/combinations/13--11Copy
    <a href="https://calculat.io/en/number/combinations/13--11">13 Choose 11: Combinations C(13, 11) - Calculatio</a>Copy
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    13 Choose 11: Combinations C(13, 11). 13 choose 11 = 78: the number of ways to choose 11 of 13 items when order doesn't matter and nothing repeats. C(13, 11) = (13 × 12) / (2 × 1).
    https://calculat.io/en/number/combinations/13--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 13 choose 11?

    13 choose 11 is 78

    Why is 13 choose 11 the same as 13 choose 2?

    Every way to choose 11 of 13 items leaves exactly 2 behind, so choosing 11 and choosing which 2 to leave out are the same count: 13 choose 11 = 13 choose 2 = 78. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(13, 11) = 3,113,510,400. Each of the 78 combinations can be put in order in 11! = 39,916,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also