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    7 Choose 4

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

    What is 7 choose 4?

    Answer

    7 choose 4 is
    35

    Order doesn't matter, no repeats: 35 ways to choose 4 of 7 items.

    Choosing 4 of 7 is the same as leaving 3 out: C(7, 4) = C(7, 3).

    C(7, 4) = 7! / (4! · 3!)

    = C(7, 3)

    = (7 × 6 × 5) / (3 × 2 × 1)
    = 210 / 6

    = 35

    If order matters (permutations): P(7, 4) = 7 × 6 × 5 × 4 = 840 — each combination in 4! = 24 orders.

    Row 7 of Pascal's triangle
    k7 choose k
    01
    17
    221
    335
    435
    521
    67
    71

    Row sum: 27 = 128 — all subsets of 7 items.

    See Also

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    https://calculat.io/en/number/combinations/7--4Copy
    <a href="https://calculat.io/en/number/combinations/7--4">7 Choose 4: Combinations C(7, 4) - Calculatio</a>Copy
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    7 Choose 4: Combinations C(7, 4). 7 choose 4 = 35: the number of ways to choose 4 of 7 items when order doesn't matter and nothing repeats. C(7, 4) = (7 × 6 × 5) / (3 × 2 × 1).
    https://calculat.io/en/number/combinations/7--4/generated.jpgCopy

    n choose 4 for other n

    n choose 4Answer
    1 choose 40
    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
    Recalculate with different values ↑

    FAQ

    What is 7 choose 4?

    7 choose 4 is 35

    Why is 7 choose 4 the same as 7 choose 3?

    Every way to choose 4 of 7 items leaves exactly 3 behind, so choosing 4 and choosing which 3 to leave out are the same count: 7 choose 4 = 7 choose 3 = 35. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(7, 4) = 840. Each of the 35 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also