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    12 Choose 6

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

    What is 12 choose 6?

    Answer

    12 choose 6 is
    924

    Order doesn't matter, no repeats: 924 ways to choose 6 of 12 items.

    C(12, 6) = 12! / (6! · 6!)

    = (12 × 11 × 10 × 9 × 8 × 7) / (6 × 5 × 4 × 3 × 2 × 1)
    = 665,280 / 720

    = 924

    If order matters (permutations): P(12, 6) = 12 × 11 × 10 × 9 × 8 × 7 = 665,280 — each combination in 6! = 720 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.

    See Also

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    https://calculat.io/en/number/combinations/12--6Copy
    <a href="https://calculat.io/en/number/combinations/12--6">12 Choose 6: Combinations C(12, 6) - Calculatio</a>Copy
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    12 Choose 6: Combinations C(12, 6). 12 choose 6 = 924: the number of ways to choose 6 of 12 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/12--6/generated.jpgCopy

    n choose 6 for other n

    n choose 6Answer
    6 choose 61
    7 choose 67
    8 choose 628
    9 choose 684
    10 choose 6210
    11 choose 6462
    12 choose 6924
    13 choose 61,716
    14 choose 63,003
    15 choose 65,005
    16 choose 68,008
    17 choose 612,376
    18 choose 618,564
    19 choose 627,132
    20 choose 638,760
    Recalculate with different values ↑

    FAQ

    What is 12 choose 6?

    12 choose 6 is 924

    Why is 12 choose 6 the largest number in row 12?

    In row 12 of Pascal's triangle the numbers grow towards the middle and shrink after it, because n choose k = n choose (n − k). With an even n the middle is k = 6, so 12 choose 6 = 924 is the largest: 12 choose 5 is only 792.

    How many ways are there if order matters?

    P(12, 6) = 665,280. Each of the 924 combinations can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also