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    15 Choose 6

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

    What is 15 choose 6?

    Answer

    15 choose 6 is
    5,005

    Order doesn't matter, no repeats: 5,005 ways to choose 6 of 15 items.

    C(15, 6) = 15! / (6! · 9!)

    = (15 × 14 × 13 × 12 × 11 × 10) / (6 × 5 × 4 × 3 × 2 × 1)
    = 3,603,600 / 720

    = 5,005

    If order matters (permutations): P(15, 6) = 15 × 14 × 13 × 12 × 11 × 10 = 3,603,600 — each combination in 6! = 720 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.

    See Also

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    https://calculat.io/en/number/combinations/15--6Copy
    <a href="https://calculat.io/en/number/combinations/15--6">15 Choose 6: Combinations C(15, 6) - Calculatio</a>Copy
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    15 Choose 6: Combinations C(15, 6). 15 choose 6 = 5,005: the number of ways to choose 6 of 15 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/15--6/generated.jpgCopy

    n choose 6 for other n

    n choose 6Answer
    6 choose 61
    7 choose 67
    8 choose 628
    9 choose 684
    10 choose 6210
    11 choose 6462
    12 choose 6924
    13 choose 61,716
    14 choose 63,003
    15 choose 65,005
    16 choose 68,008
    17 choose 612,376
    18 choose 618,564
    19 choose 627,132
    20 choose 638,760
    Recalculate with different values ↑

    FAQ

    What is 15 choose 6?

    15 choose 6 is 5,005

    Why is 15 choose 6 the same as 15 choose 9?

    Every way to choose 6 of 15 items leaves exactly 9 behind, so choosing 6 and choosing which 9 to leave out are the same count: 15 choose 6 = 15 choose 9 = 5,005. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(15, 6) = 3,603,600. Each of the 5,005 combinations can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also