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    15 Choose 15

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

    What is 15 choose 15?

    Answer

    15 choose 15 is
    1

    Order doesn't matter, no repeats: 1 way to choose 15 of 15 items.

    There is exactly one way: take all.

    C(15, 15) = 15! / (15! · 0!)

    = 1

    0! = 1 (an empty product), so 15! cancels out completely.

    If order matters (permutations): P(15, 15) = 15 × 14 × 13 × … × 1 = 1,307,674,368,000 — each combination in 15! = 1,307,674,368,000 orders.

    Row 15 of Pascal's triangle
    k15 choose k
    01
    115
    2105
    3455
    41,365
    53,003
    65,005
    76,435
    86,435
    95,005
    103,003
    111,365
    12455
    13105
    1415
    151

    Row sum: 215 = 32,768 — all subsets of 15 items.

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

    15 choose 15 is 1

    Why is 15 choose 15 the same as 15 choose 0?

    Every way to choose 15 of 15 items leaves exactly 0 behind, so choosing 15 and choosing which 0 to leave out are the same count: 15 choose 15 = 15 choose 0 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(15, 15) = 1,307,674,368,000. The only combination — all 15 items — 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