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    16 Choose 4

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

    What is 16 choose 4?

    Answer

    16 choose 4 is
    1,820

    Order doesn't matter, no repeats: 1,820 ways to choose 4 of 16 items.

    C(16, 4) = 16! / (4! · 12!)

    = (16 × 15 × 14 × 13) / (4 × 3 × 2 × 1)
    = 43,680 / 24

    = 1,820

    If order matters (permutations): P(16, 4) = 16 × 15 × 14 × 13 = 43,680 — each combination in 4! = 24 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--4Copy
    <a href="https://calculat.io/en/number/combinations/16--4">16 Choose 4: Combinations C(16, 4) - Calculatio</a>Copy
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    16 Choose 4: Combinations C(16, 4). 16 choose 4 = 1,820: the number of ways to choose 4 of 16 items when order doesn't matter and nothing repeats. C(16, 4) = (16 × 15 × 14 × 13) / (4 × 3 × 2 × 1).
    https://calculat.io/en/number/combinations/16--4/generated.jpgCopy

    n choose 4 for other n

    n choose 4Answer
    7 choose 435
    8 choose 470
    9 choose 4126
    10 choose 4210
    11 choose 4330
    12 choose 4495
    13 choose 4715
    14 choose 41,001
    15 choose 41,365
    16 choose 41,820
    17 choose 42,380
    18 choose 43,060
    19 choose 43,876
    20 choose 44,845
    24 choose 410,626
    Recalculate with different values ↑

    FAQ

    What is 16 choose 4?

    16 choose 4 is 1,820

    Why is 16 choose 4 the same as 16 choose 12?

    Every way to choose 4 of 16 items leaves exactly 12 behind, so choosing 4 and choosing which 12 to leave out are the same count: 16 choose 4 = 16 choose 12 = 1,820. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(16, 4) = 43,680. Each of the 1,820 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also