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    20 Choose 4

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

    What is 20 choose 4?

    Answer

    20 choose 4 is
    4,845

    Order doesn't matter, no repeats: 4,845 ways to choose 4 of 20 items.

    C(20, 4) = 20! / (4! · 16!)

    = (20 × 19 × 18 × 17) / (4 × 3 × 2 × 1)
    = 116,280 / 24

    = 4,845

    If order matters (permutations): P(20, 4) = 20 × 19 × 18 × 17 = 116,280 — each combination in 4! = 24 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.

    See Also

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    https://calculat.io/en/number/combinations/20--4Copy
    <a href="https://calculat.io/en/number/combinations/20--4">20 Choose 4: Combinations C(20, 4) - Calculatio</a>Copy
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    20 Choose 4: Combinations C(20, 4). 20 choose 4 = 4,845: the number of ways to choose 4 of 20 items when order doesn't matter and nothing repeats. C(20, 4) = (20 × 19 × 18 × 17) / (4 × 3 × 2 × 1).
    https://calculat.io/en/number/combinations/20--4/generated.jpgCopy

    n choose 4 for other n

    n choose 4Answer
    7 choose 435
    8 choose 470
    9 choose 4126
    10 choose 4210
    11 choose 4330
    12 choose 4495
    13 choose 4715
    14 choose 41,001
    15 choose 41,365
    16 choose 41,820
    17 choose 42,380
    18 choose 43,060
    19 choose 43,876
    20 choose 44,845
    24 choose 410,626
    Recalculate with different values ↑

    FAQ

    What is 20 choose 4?

    20 choose 4 is 4,845

    Why is 20 choose 4 the same as 20 choose 16?

    Every way to choose 4 of 20 items leaves exactly 16 behind, so choosing 4 and choosing which 16 to leave out are the same count: 20 choose 4 = 20 choose 16 = 4,845. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(20, 4) = 116,280. Each of the 4,845 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also