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    16 Choose 5

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

    What is 16 choose 5?

    Answer

    16 choose 5 is
    4,368

    Order doesn't matter, no repeats: 4,368 ways to choose 5 of 16 items.

    C(16, 5) = 16! / (5! · 11!)

    = (16 × 15 × 14 × 13 × 12) / (5 × 4 × 3 × 2 × 1)
    = 524,160 / 120

    = 4,368

    If order matters (permutations): P(16, 5) = 16 × 15 × 14 × 13 × 12 = 524,160 — each combination in 5! = 120 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--5Copy
    <a href="https://calculat.io/en/number/combinations/16--5">16 Choose 5: Combinations C(16, 5) - Calculatio</a>Copy
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    16 Choose 5: Combinations C(16, 5). 16 choose 5 = 4,368: the number of ways to choose 5 of 16 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/16--5/generated.jpgCopy

    n choose 5 for other n

    n choose 5Answer
    6 choose 56
    7 choose 521
    8 choose 556
    9 choose 5126
    10 choose 5252
    11 choose 5462
    12 choose 5792
    13 choose 51,287
    14 choose 52,002
    15 choose 53,003
    16 choose 54,368
    17 choose 56,188
    18 choose 58,568
    19 choose 511,628
    20 choose 515,504
    Recalculate with different values ↑

    FAQ

    What is 16 choose 5?

    16 choose 5 is 4,368

    Why is 16 choose 5 the same as 16 choose 11?

    Every way to choose 5 of 16 items leaves exactly 11 behind, so choosing 5 and choosing which 11 to leave out are the same count: 16 choose 5 = 16 choose 11 = 4,368. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(16, 5) = 524,160. Each of the 4,368 combinations can be put in order in 5! = 120 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also