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    16 Choose 8

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

    What is 16 choose 8?

    Answer

    16 choose 8 is
    12,870

    Order doesn't matter, no repeats: 12,870 ways to choose 8 of 16 items.

    C(16, 8) = 16! / (8! · 8!)

    = (16 × 15 × 14 × … × 9) / (8 × 7 × 6 × … × 1)

    8 factors on top and bottom

    = 518,918,400 / 40,320

    = 12,870

    If order matters (permutations): P(16, 8) = 16 × 15 × 14 × … × 9 = 518,918,400 — each combination in 8! = 40,320 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--8Copy
    <a href="https://calculat.io/en/number/combinations/16--8">16 Choose 8: Combinations C(16, 8) - Calculatio</a>Copy
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    16 Choose 8: Combinations C(16, 8). 16 choose 8 = 12,870: the number of ways to choose 8 of 16 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/16--8/generated.jpgCopy

    n choose 8 for other n

    n choose 8Answer
    8 choose 81
    9 choose 89
    10 choose 845
    11 choose 8165
    12 choose 8495
    13 choose 81,287
    14 choose 83,003
    15 choose 86,435
    16 choose 812,870
    17 choose 824,310
    18 choose 843,758
    19 choose 875,582
    20 choose 8125,970
    Recalculate with different values ↑

    FAQ

    What is 16 choose 8?

    16 choose 8 is 12,870

    Why is 16 choose 8 the largest number in row 16?

    In row 16 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 = 8, so 16 choose 8 = 12,870 is the largest: 16 choose 7 is only 11,440.

    How many ways are there if order matters?

    P(16, 8) = 518,918,400. Each of the 12,870 combinations can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also