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    16 Choose 15

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

    What is 16 choose 15?

    Answer

    16 choose 15 is
    16

    Order doesn't matter, no repeats: 16 ways to choose 15 of 16 items.

    Choosing 15 of 16 is the same as leaving 1 out: C(16, 15) = C(16, 1).

    C(16, 15) = 16! / (15! · 1!)

    = C(16, 1)

    = 16 / 1

    = 16

    If order matters (permutations): P(16, 15) = 16 × 15 × 14 × … × 2 = 20,922,789,888,000 — each combination in 15! = 1,307,674,368,000 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--15Copy
    <a href="https://calculat.io/en/number/combinations/16--15">16 Choose 15: Combinations C(16, 15) - Calculatio</a>Copy
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    16 Choose 15: Combinations C(16, 15). 16 choose 15 = 16: the number of ways to choose 15 of 16 items when order doesn't matter and nothing repeats. C(16, 15) = 16 / 1.
    https://calculat.io/en/number/combinations/16--15/generated.jpgCopy

    n choose 15 for other n

    n choose 15Answer
    15 choose 151
    16 choose 1516
    17 choose 15136
    18 choose 15816
    19 choose 153,876
    20 choose 1515,504
    Recalculate with different values ↑

    FAQ

    What is 16 choose 15?

    16 choose 15 is 16

    Why is 16 choose 15 the same as 16 choose 1?

    Every way to choose 15 of 16 items leaves exactly 1 behind, so choosing 15 and choosing which one to leave out are the same count: 16 choose 15 = 16 choose 1 = 16. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(16, 15) = 20,922,789,888,000. Each of the 16 combinations can be put in order in 15! = 1,307,674,368,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also