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    17 Choose 15

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

    What is 17 choose 15?

    Answer

    17 choose 15 is
    136

    Order doesn't matter, no repeats: 136 ways to choose 15 of 17 items.

    Choosing 15 of 17 is the same as leaving 2 out: C(17, 15) = C(17, 2).

    C(17, 15) = 17! / (15! · 2!)

    = C(17, 2)

    = (17 × 16) / (2 × 1)
    = 272 / 2

    = 136

    If order matters (permutations): P(17, 15) = 17 × 16 × 15 × … × 3 = 177,843,714,048,000 — each combination in 15! = 1,307,674,368,000 orders.

    Row 17 of Pascal's triangle
    k17 choose k
    01
    117
    2136
    3680
    42,380
    56,188
    612,376
    719,448
    824,310
    924,310
    1019,448
    1112,376
    126,188
    132,380
    14680
    15136
    1617
    171

    Row sum: 217 = 131,072 — all subsets of 17 items.

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    https://calculat.io/en/number/combinations/17--15Copy
    <a href="https://calculat.io/en/number/combinations/17--15">17 Choose 15: Combinations C(17, 15) - Calculatio</a>Copy
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    17 Choose 15: Combinations C(17, 15). 17 choose 15 = 136: the number of ways to choose 15 of 17 items when order doesn't matter and nothing repeats. C(17, 15) = (17 × 16) / (2 × 1).
    https://calculat.io/en/number/combinations/17--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 17 choose 15?

    17 choose 15 is 136

    Why is 17 choose 15 the same as 17 choose 2?

    Every way to choose 15 of 17 items leaves exactly 2 behind, so choosing 15 and choosing which 2 to leave out are the same count: 17 choose 15 = 17 choose 2 = 136. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(17, 15) = 177,843,714,048,000. Each of the 136 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