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    16 Choose 13

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

    What is 16 choose 13?

    Answer

    16 choose 13 is
    560

    Order doesn't matter, no repeats: 560 ways to choose 13 of 16 items.

    Choosing 13 of 16 is the same as leaving 3 out: C(16, 13) = C(16, 3).

    C(16, 13) = 16! / (13! · 3!)

    = C(16, 3)

    = (16 × 15 × 14) / (3 × 2 × 1)
    = 3,360 / 6

    = 560

    If order matters (permutations): P(16, 13) = 16 × 15 × 14 × … × 4 = 3,487,131,648,000 — each combination in 13! = 6,227,020,800 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.

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    https://calculat.io/en/number/combinations/16--13Copy
    <a href="https://calculat.io/en/number/combinations/16--13">16 Choose 13: Combinations C(16, 13) - Calculatio</a>Copy
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    16 Choose 13: Combinations C(16, 13). 16 choose 13 = 560: the number of ways to choose 13 of 16 items when order doesn't matter and nothing repeats. C(16, 13) = (16 × 15 × 14) / (3 × 2 × 1).
    https://calculat.io/en/number/combinations/16--13/generated.jpgCopy

    n choose 13 for other n

    n choose 13Answer
    13 choose 131
    14 choose 1314
    15 choose 13105
    16 choose 13560
    17 choose 132,380
    18 choose 138,568
    19 choose 1327,132
    20 choose 1377,520
    Recalculate with different values ↑

    FAQ

    What is 16 choose 13?

    16 choose 13 is 560

    Why is 16 choose 13 the same as 16 choose 3?

    Every way to choose 13 of 16 items leaves exactly 3 behind, so choosing 13 and choosing which 3 to leave out are the same count: 16 choose 13 = 16 choose 3 = 560. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(16, 13) = 3,487,131,648,000. Each of the 560 combinations can be put in order in 13! = 6,227,020,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also