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    4 Choose 4

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

    What is 4 choose 4?

    Answer

    4 choose 4 is
    1

    Order doesn't matter, no repeats: 1 way to choose 4 of 4 items.

    There is exactly one way: take all.

    C(4, 4) = 4! / (4! · 0!)

    = 1

    0! = 1 (an empty product), so 4! cancels out completely.

    If order matters (permutations): P(4, 4) = 4 × 3 × 2 × 1 = 24 — each combination in 4! = 24 orders.

    Row 4 of Pascal's triangle
    k4 choose k
    01
    14
    26
    34
    41

    Row sum: 24 = 16 — all subsets of 4 items.

    See Also

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

    4 choose 4 is 1

    Why is 4 choose 4 the same as 4 choose 0?

    Every way to choose 4 of 4 items leaves exactly 0 behind, so choosing 4 and choosing which 0 to leave out are the same count: 4 choose 4 = 4 choose 0 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(4, 4) = 24. The only combination — all 4 items — can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also