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    12 Choose 4

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

    What is 12 choose 4?

    Answer

    12 choose 4 is
    495

    Order doesn't matter, no repeats: 495 ways to choose 4 of 12 items.

    C(12, 4) = 12! / (4! · 8!)

    = (12 × 11 × 10 × 9) / (4 × 3 × 2 × 1)
    = 11,880 / 24

    = 495

    If order matters (permutations): P(12, 4) = 12 × 11 × 10 × 9 = 11,880 — each combination in 4! = 24 orders.

    Row 12 of Pascal's triangle
    k12 choose k
    01
    112
    266
    3220
    4495
    5792
    6924
    7792
    8495
    9220
    1066
    1112
    121

    Row sum: 212 = 4,096 — all subsets of 12 items.

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    https://calculat.io/en/number/combinations/12--4Copy
    <a href="https://calculat.io/en/number/combinations/12--4">12 Choose 4: Combinations C(12, 4) - Calculatio</a>Copy
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    12 Choose 4: Combinations C(12, 4). 12 choose 4 = 495: the number of ways to choose 4 of 12 items when order doesn't matter and nothing repeats. C(12, 4) = (12 × 11 × 10 × 9) / (4 × 3 × 2 × 1).
    https://calculat.io/en/number/combinations/12--4/generated.jpgCopy

    n choose 4 for other n

    n choose 4Answer
    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
    17 choose 42,380
    18 choose 43,060
    19 choose 43,876
    Recalculate with different values ↑

    FAQ

    What is 12 choose 4?

    12 choose 4 is 495

    Why is 12 choose 4 the same as 12 choose 8?

    Every way to choose 4 of 12 items leaves exactly 8 behind, so choosing 4 and choosing which 8 to leave out are the same count: 12 choose 4 = 12 choose 8 = 495. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(12, 4) = 11,880. Each of the 495 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also