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    15 Choose 4

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

    What is 15 choose 4?

    Answer

    15 choose 4 is
    1,365

    Order doesn't matter, no repeats: 1,365 ways to choose 4 of 15 items.

    C(15, 4) = 15! / (4! · 11!)

    = (15 × 14 × 13 × 12) / (4 × 3 × 2 × 1)
    = 32,760 / 24

    = 1,365

    If order matters (permutations): P(15, 4) = 15 × 14 × 13 × 12 = 32,760 — each combination in 4! = 24 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--4Copy
    <a href="https://calculat.io/en/number/combinations/15--4">15 Choose 4: Combinations C(15, 4) - Calculatio</a>Copy
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    15 Choose 4: Combinations C(15, 4). 15 choose 4 = 1,365: the number of ways to choose 4 of 15 items when order doesn't matter and nothing repeats. C(15, 4) = (15 × 14 × 13 × 12) / (4 × 3 × 2 × 1).
    https://calculat.io/en/number/combinations/15--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 15 choose 4?

    15 choose 4 is 1,365

    Why is 15 choose 4 the same as 15 choose 11?

    Every way to choose 4 of 15 items leaves exactly 11 behind, so choosing 4 and choosing which 11 to leave out are the same count: 15 choose 4 = 15 choose 11 = 1,365. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(15, 4) = 32,760. Each of the 1,365 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also