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    24 Choose 4

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

    What is 24 choose 4?

    Answer

    24 choose 4 is
    10,626

    Order doesn't matter, no repeats: 10,626 ways to choose 4 of 24 items.

    C(24, 4) = 24! / (4! · 20!)

    = (24 × 23 × 22 × 21) / (4 × 3 × 2 × 1)
    = 255,024 / 24

    = 10,626

    If order matters (permutations): P(24, 4) = 24 × 23 × 22 × 21 = 255,024 — each combination in 4! = 24 orders.

    Row 24 of Pascal's triangle
    k24 choose k
    01
    124
    2276
    32,024
    410,626
    542,504
    6134,596
    7346,104
    ……
    241

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    https://calculat.io/en/number/combinations/24--4Copy
    <a href="https://calculat.io/en/number/combinations/24--4">24 Choose 4: Combinations C(24, 4) - Calculatio</a>Copy
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    24 Choose 4: Combinations C(24, 4). 24 choose 4 = 10,626: the number of ways to choose 4 of 24 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/24--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 24 choose 4?

    24 choose 4 is 10,626

    Why is 24 choose 4 the same as 24 choose 20?

    Every way to choose 4 of 24 items leaves exactly 20 behind, so choosing 4 and choosing which 20 to leave out are the same count: 24 choose 4 = 24 choose 20 = 10,626. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(24, 4) = 255,024. Each of the 10,626 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also