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    17 Choose 12

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

    What is 17 choose 12?

    Answer

    17 choose 12 is
    6,188

    Order doesn't matter, no repeats: 6,188 ways to choose 12 of 17 items.

    Choosing 12 of 17 is the same as leaving 5 out: C(17, 12) = C(17, 5).

    C(17, 12) = 17! / (12! · 5!)

    = C(17, 5)

    = (17 × 16 × 15 × 14 × 13) / (5 × 4 × 3 × 2 × 1)
    = 742,560 / 120

    = 6,188

    If order matters (permutations): P(17, 12) = 17 × 16 × 15 × … × 6 = 2,964,061,900,800 — each combination in 12! = 479,001,600 orders.

    Row 17 of Pascal's triangle
    k17 choose k
    01
    117
    2136
    3680
    42,380
    56,188
    612,376
    719,448
    824,310
    924,310
    1019,448
    1112,376
    126,188
    132,380
    14680
    15136
    1617
    171

    Row sum: 217 = 131,072 — all subsets of 17 items.

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    https://calculat.io/en/number/combinations/17--12Copy
    <a href="https://calculat.io/en/number/combinations/17--12">17 Choose 12: Combinations C(17, 12) - Calculatio</a>Copy
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    17 Choose 12: Combinations C(17, 12). 17 choose 12 = 6,188: the number of ways to choose 12 of 17 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/17--12/generated.jpgCopy

    n choose 12 for other n

    n choose 12Answer
    12 choose 121
    13 choose 1213
    14 choose 1291
    15 choose 12455
    16 choose 121,820
    17 choose 126,188
    18 choose 1218,564
    19 choose 1250,388
    20 choose 12125,970
    Recalculate with different values ↑

    FAQ

    What is 17 choose 12?

    17 choose 12 is 6,188

    Why is 17 choose 12 the same as 17 choose 5?

    Every way to choose 12 of 17 items leaves exactly 5 behind, so choosing 12 and choosing which 5 to leave out are the same count: 17 choose 12 = 17 choose 5 = 6,188. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(17, 12) = 2,964,061,900,800. Each of the 6,188 combinations can be put in order in 12! = 479,001,600 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also