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    16 Choose 6

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

    What is 16 choose 6?

    Answer

    16 choose 6 is
    8,008

    Order doesn't matter, no repeats: 8,008 ways to choose 6 of 16 items.

    C(16, 6) = 16! / (6! · 10!)

    = (16 × 15 × 14 × 13 × 12 × 11) / (6 × 5 × 4 × 3 × 2 × 1)
    = 5,765,760 / 720

    = 8,008

    If order matters (permutations): P(16, 6) = 16 × 15 × 14 × 13 × 12 × 11 = 5,765,760 — each combination in 6! = 720 orders.

    Row 16 of Pascal's triangle
    k16 choose k
    01
    116
    2120
    3560
    41,820
    54,368
    68,008
    711,440
    812,870
    911,440
    108,008
    114,368
    121,820
    13560
    14120
    1516
    161

    Row sum: 216 = 65,536 — all subsets of 16 items.

    See Also

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    https://calculat.io/en/number/combinations/16--6Copy
    <a href="https://calculat.io/en/number/combinations/16--6">16 Choose 6: Combinations C(16, 6) - Calculatio</a>Copy
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    16 Choose 6: Combinations C(16, 6). 16 choose 6 = 8,008: the number of ways to choose 6 of 16 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/16--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 16 choose 6?

    16 choose 6 is 8,008

    Why is 16 choose 6 the same as 16 choose 10?

    Every way to choose 6 of 16 items leaves exactly 10 behind, so choosing 6 and choosing which 10 to leave out are the same count: 16 choose 6 = 16 choose 10 = 8,008. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(16, 6) = 5,765,760. Each of the 8,008 combinations can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also