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    20 Choose 9

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

    What is 20 choose 9?

    Answer

    20 choose 9 is
    167,960

    Order doesn't matter, no repeats: 167,960 ways to choose 9 of 20 items.

    C(20, 9) = 20! / (9! · 11!)

    = (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, 9) = 20 × 19 × 18 × … × 12 = 60,949,324,800 — each combination in 9! = 362,880 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--9Copy
    <a href="https://calculat.io/en/number/combinations/20--9">20 Choose 9: Combinations C(20, 9) - Calculatio</a>Copy
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    20 Choose 9: Combinations C(20, 9). 20 choose 9 = 167,960: the number of ways to choose 9 of 20 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/20--9/generated.jpgCopy

    n choose 9 for other n

    n choose 9Answer
    9 choose 91
    10 choose 910
    11 choose 955
    12 choose 9220
    13 choose 9715
    14 choose 92,002
    15 choose 95,005
    16 choose 911,440
    17 choose 924,310
    18 choose 948,620
    19 choose 992,378
    20 choose 9167,960
    Recalculate with different values ↑

    FAQ

    What is 20 choose 9?

    20 choose 9 is 167,960

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

    Every way to choose 9 of 20 items leaves exactly 11 behind, so choosing 9 and choosing which 11 to leave out are the same count: 20 choose 9 = 20 choose 11 = 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, 9) = 60,949,324,800. Each of the 167,960 combinations can be put in order in 9! = 362,880 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also