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    17 Choose 6

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

    What is 17 choose 6?

    Answer

    17 choose 6 is
    12,376

    Order doesn't matter, no repeats: 12,376 ways to choose 6 of 17 items.

    C(17, 6) = 17! / (6! · 11!)

    = (17 × 16 × 15 × 14 × 13 × 12) / (6 × 5 × 4 × 3 × 2 × 1)
    = 8,910,720 / 720

    = 12,376

    If order matters (permutations): P(17, 6) = 17 × 16 × 15 × 14 × 13 × 12 = 8,910,720 — each combination in 6! = 720 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--6Copy
    <a href="https://calculat.io/en/number/combinations/17--6">17 Choose 6: Combinations C(17, 6) - Calculatio</a>Copy
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    17 Choose 6: Combinations C(17, 6). 17 choose 6 = 12,376: the number of ways to choose 6 of 17 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/17--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 17 choose 6?

    17 choose 6 is 12,376

    Why is 17 choose 6 the same as 17 choose 11?

    Every way to choose 6 of 17 items leaves exactly 11 behind, so choosing 6 and choosing which 11 to leave out are the same count: 17 choose 6 = 17 choose 11 = 12,376. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(17, 6) = 8,910,720. Each of the 12,376 combinations can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also