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    17 Choose 14

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

    What is 17 choose 14?

    Answer

    17 choose 14 is
    680

    Order doesn't matter, no repeats: 680 ways to choose 14 of 17 items.

    Choosing 14 of 17 is the same as leaving 3 out: C(17, 14) = C(17, 3).

    C(17, 14) = 17! / (14! · 3!)

    = C(17, 3)

    = (17 × 16 × 15) / (3 × 2 × 1)
    = 4,080 / 6

    = 680

    If order matters (permutations): P(17, 14) = 17 × 16 × 15 × … × 4 = 59,281,238,016,000 — each combination in 14! = 87,178,291,200 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--14Copy
    <a href="https://calculat.io/en/number/combinations/17--14">17 Choose 14: Combinations C(17, 14) - Calculatio</a>Copy
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    17 Choose 14: Combinations C(17, 14). 17 choose 14 = 680: the number of ways to choose 14 of 17 items when order doesn't matter and nothing repeats. C(17, 14) = (17 × 16 × 15) / (3 × 2 × 1).
    https://calculat.io/en/number/combinations/17--14/generated.jpgCopy

    n choose 14 for other n

    n choose 14Answer
    14 choose 141
    15 choose 1415
    16 choose 14120
    17 choose 14680
    18 choose 143,060
    19 choose 1411,628
    20 choose 1438,760
    Recalculate with different values ↑

    FAQ

    What is 17 choose 14?

    17 choose 14 is 680

    Why is 17 choose 14 the same as 17 choose 3?

    Every way to choose 14 of 17 items leaves exactly 3 behind, so choosing 14 and choosing which 3 to leave out are the same count: 17 choose 14 = 17 choose 3 = 680. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(17, 14) = 59,281,238,016,000. Each of the 680 combinations can be put in order in 14! = 87,178,291,200 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also