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    17 Choose 8

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

    What is 17 choose 8?

    Answer

    17 choose 8 is
    24,310

    Order doesn't matter, no repeats: 24,310 ways to choose 8 of 17 items.

    C(17, 8) = 17! / (8! · 9!)

    = (17 × 16 × 15 × … × 10) / (8 × 7 × 6 × … × 1)

    8 factors on top and bottom

    = 980,179,200 / 40,320

    = 24,310

    If order matters (permutations): P(17, 8) = 17 × 16 × 15 × … × 10 = 980,179,200 — each combination in 8! = 40,320 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--8Copy
    <a href="https://calculat.io/en/number/combinations/17--8">17 Choose 8: Combinations C(17, 8) - Calculatio</a>Copy
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    17 Choose 8: Combinations C(17, 8). 17 choose 8 = 24,310: the number of ways to choose 8 of 17 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/17--8/generated.jpgCopy

    n choose 8 for other n

    n choose 8Answer
    8 choose 81
    9 choose 89
    10 choose 845
    11 choose 8165
    12 choose 8495
    13 choose 81,287
    14 choose 83,003
    15 choose 86,435
    16 choose 812,870
    17 choose 824,310
    18 choose 843,758
    19 choose 875,582
    20 choose 8125,970
    Recalculate with different values ↑

    FAQ

    What is 17 choose 8?

    17 choose 8 is 24,310

    Why is 17 choose 8 the same as 17 choose 9?

    Every way to choose 8 of 17 items leaves exactly 9 behind, so choosing 8 and choosing which 9 to leave out are the same count: 17 choose 8 = 17 choose 9 = 24,310. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(17, 8) = 980,179,200. Each of the 24,310 combinations can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also