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    9 Choose 4

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

    What is 9 choose 4?

    Answer

    9 choose 4 is
    126

    Order doesn't matter, no repeats: 126 ways to choose 4 of 9 items.

    C(9, 4) = 9! / (4! · 5!)

    = (9 × 8 × 7 × 6) / (4 × 3 × 2 × 1)
    = 3,024 / 24

    = 126

    If order matters (permutations): P(9, 4) = 9 × 8 × 7 × 6 = 3,024 — each combination in 4! = 24 orders.

    Row 9 of Pascal's triangle
    k9 choose k
    01
    19
    236
    384
    4126
    5126
    684
    736
    89
    91

    Row sum: 29 = 512 — all subsets of 9 items.

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    https://calculat.io/en/number/combinations/9--4Copy
    <a href="https://calculat.io/en/number/combinations/9--4">9 Choose 4: Combinations C(9, 4) - Calculatio</a>Copy
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    9 Choose 4: Combinations C(9, 4). 9 choose 4 = 126: the number of ways to choose 4 of 9 items when order doesn't matter and nothing repeats. C(9, 4) = (9 × 8 × 7 × 6) / (4 × 3 × 2 × 1).
    https://calculat.io/en/number/combinations/9--4/generated.jpgCopy

    n choose 4 for other n

    n choose 4Answer
    2 choose 40
    3 choose 40
    4 choose 41
    5 choose 45
    6 choose 415
    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
    Recalculate with different values ↑

    FAQ

    What is 9 choose 4?

    9 choose 4 is 126

    Why is 9 choose 4 the same as 9 choose 5?

    Every way to choose 4 of 9 items leaves exactly 5 behind, so choosing 4 and choosing which 5 to leave out are the same count: 9 choose 4 = 9 choose 5 = 126. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(9, 4) = 3,024. Each of the 126 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also