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    17 Choose 13

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

    What is 17 choose 13?

    Answer

    17 choose 13 is
    2,380

    Order doesn't matter, no repeats: 2,380 ways to choose 13 of 17 items.

    Choosing 13 of 17 is the same as leaving 4 out: C(17, 13) = C(17, 4).

    C(17, 13) = 17! / (13! · 4!)

    = C(17, 4)

    = (17 × 16 × 15 × 14) / (4 × 3 × 2 × 1)
    = 57,120 / 24

    = 2,380

    If order matters (permutations): P(17, 13) = 17 × 16 × 15 × … × 5 = 14,820,309,504,000 — each combination in 13! = 6,227,020,800 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--13Copy
    <a href="https://calculat.io/en/number/combinations/17--13">17 Choose 13: Combinations C(17, 13) - Calculatio</a>Copy
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    17 Choose 13: Combinations C(17, 13). 17 choose 13 = 2,380: the number of ways to choose 13 of 17 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/17--13/generated.jpgCopy

    n choose 13 for other n

    n choose 13Answer
    13 choose 131
    14 choose 1314
    15 choose 13105
    16 choose 13560
    17 choose 132,380
    18 choose 138,568
    19 choose 1327,132
    20 choose 1377,520
    Recalculate with different values ↑

    FAQ

    What is 17 choose 13?

    17 choose 13 is 2,380

    Why is 17 choose 13 the same as 17 choose 4?

    Every way to choose 13 of 17 items leaves exactly 4 behind, so choosing 13 and choosing which 4 to leave out are the same count: 17 choose 13 = 17 choose 4 = 2,380. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(17, 13) = 14,820,309,504,000. Each of the 2,380 combinations can be put in order in 13! = 6,227,020,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also