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    20 Choose 11

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

    What is 20 choose 11?

    Answer

    20 choose 11 is
    167,960

    Order doesn't matter, no repeats: 167,960 ways to choose 11 of 20 items.

    Choosing 11 of 20 is the same as leaving 9 out: C(20, 11) = C(20, 9).

    C(20, 11) = 20! / (11! · 9!)

    = C(20, 9)

    = (20 × 19 × 18 × … × 12) / (9 × 8 × 7 × … × 1)

    9 factors on top and bottom

    = 60,949,324,800 / 362,880

    = 167,960

    If order matters (permutations): P(20, 11) = 20 × 19 × 18 × … × 10 = 6,704,425,728,000 — each combination in 11! = 39,916,800 orders.

    Row 20 of Pascal's triangle
    k20 choose k
    01
    120
    2190
    31,140
    44,845
    515,504
    638,760
    777,520
    8125,970
    9167,960
    10184,756
    11167,960
    12125,970
    1377,520
    1438,760
    1515,504
    164,845
    171,140
    18190
    1920
    201

    Row sum: 220 = 1,048,576 — all subsets of 20 items.

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    https://calculat.io/en/number/combinations/20--11Copy
    <a href="https://calculat.io/en/number/combinations/20--11">20 Choose 11: Combinations C(20, 11) - Calculatio</a>Copy
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    20 Choose 11: Combinations C(20, 11). 20 choose 11 = 167,960: the number of ways to choose 11 of 20 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/20--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 20 choose 11?

    20 choose 11 is 167,960

    Why is 20 choose 11 the same as 20 choose 9?

    Every way to choose 11 of 20 items leaves exactly 9 behind, so choosing 11 and choosing which 9 to leave out are the same count: 20 choose 11 = 20 choose 9 = 167,960. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(20, 11) = 6,704,425,728,000. Each of the 167,960 combinations can be put in order in 11! = 39,916,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also