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    6 Choose 4

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

    What is 6 choose 4?

    Answer

    6 choose 4 is
    15

    Order doesn't matter, no repeats: 15 ways to choose 4 of 6 items.

    Choosing 4 of 6 is the same as leaving 2 out: C(6, 4) = C(6, 2).

    C(6, 4) = 6! / (4! · 2!)

    = C(6, 2)

    = (6 × 5) / (2 × 1)
    = 30 / 2

    = 15

    If order matters (permutations): P(6, 4) = 6 × 5 × 4 × 3 = 360 — each combination in 4! = 24 orders.

    Row 6 of Pascal's triangle
    k6 choose k
    01
    16
    215
    320
    415
    56
    61

    Row sum: 26 = 64 — all subsets of 6 items.

    See Also

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    https://calculat.io/en/number/combinations/6--4Copy
    <a href="https://calculat.io/en/number/combinations/6--4">6 Choose 4: Combinations C(6, 4) - Calculatio</a>Copy
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    6 Choose 4: Combinations C(6, 4). 6 choose 4 = 15: the number of ways to choose 4 of 6 items when order doesn't matter and nothing repeats. C(6, 4) = (6 × 5) / (2 × 1).
    https://calculat.io/en/number/combinations/6--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 6 choose 4?

    6 choose 4 is 15

    Why is 6 choose 4 the same as 6 choose 2?

    Every way to choose 4 of 6 items leaves exactly 2 behind, so choosing 4 and choosing which 2 to leave out are the same count: 6 choose 4 = 6 choose 2 = 15. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(6, 4) = 360. Each of the 15 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also