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    17 Choose 5

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

    What is 17 choose 5?

    Answer

    17 choose 5 is
    6,188

    Order doesn't matter, no repeats: 6,188 ways to choose 5 of 17 items.

    C(17, 5) = 17! / (5! · 12!)

    = (17 × 16 × 15 × 14 × 13) / (5 × 4 × 3 × 2 × 1)
    = 742,560 / 120

    = 6,188

    If order matters (permutations): P(17, 5) = 17 × 16 × 15 × 14 × 13 = 742,560 — each combination in 5! = 120 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--5Copy
    <a href="https://calculat.io/en/number/combinations/17--5">17 Choose 5: Combinations C(17, 5) - Calculatio</a>Copy
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    17 Choose 5: Combinations C(17, 5). 17 choose 5 = 6,188: the number of ways to choose 5 of 17 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/17--5/generated.jpgCopy

    n choose 5 for other n

    n choose 5Answer
    6 choose 56
    7 choose 521
    8 choose 556
    9 choose 5126
    10 choose 5252
    11 choose 5462
    12 choose 5792
    13 choose 51,287
    14 choose 52,002
    15 choose 53,003
    16 choose 54,368
    17 choose 56,188
    18 choose 58,568
    19 choose 511,628
    20 choose 515,504
    Recalculate with different values ↑

    FAQ

    What is 17 choose 5?

    17 choose 5 is 6,188

    Why is 17 choose 5 the same as 17 choose 12?

    Every way to choose 5 of 17 items leaves exactly 12 behind, so choosing 5 and choosing which 12 to leave out are the same count: 17 choose 5 = 17 choose 12 = 6,188. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(17, 5) = 742,560. Each of the 6,188 combinations can be put in order in 5! = 120 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also