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    12 Choose 3

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

    What is 12 choose 3?

    Answer

    12 choose 3 is
    220

    Order doesn't matter, no repeats: 220 ways to choose 3 of 12 items.

    C(12, 3) = 12! / (3! · 9!)

    = (12 × 11 × 10) / (3 × 2 × 1)
    = 1,320 / 6

    = 220

    If order matters (permutations): P(12, 3) = 12 × 11 × 10 = 1,320 — each combination in 3! = 6 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--3Copy
    <a href="https://calculat.io/en/number/combinations/12--3">12 Choose 3: Combinations C(12, 3) - Calculatio</a>Copy
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    12 Choose 3: Combinations C(12, 3). 12 choose 3 = 220: the number of ways to choose 3 of 12 items when order doesn't matter and nothing repeats. C(12, 3) = (12 × 11 × 10) / (3 × 2 × 1).
    https://calculat.io/en/number/combinations/12--3/generated.jpgCopy

    n choose 3 for other n

    n choose 3Answer
    5 choose 310
    6 choose 320
    7 choose 335
    8 choose 356
    9 choose 384
    10 choose 3120
    11 choose 3165
    12 choose 3220
    13 choose 3286
    14 choose 3364
    15 choose 3455
    16 choose 3560
    17 choose 3680
    18 choose 3816
    19 choose 3969
    Recalculate with different values ↑

    FAQ

    What is 12 choose 3?

    12 choose 3 is 220

    Why is 12 choose 3 the same as 12 choose 9?

    Every way to choose 3 of 12 items leaves exactly 9 behind, so choosing 3 and choosing which 9 to leave out are the same count: 12 choose 3 = 12 choose 9 = 220. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(12, 3) = 1,320. Each of the 220 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also