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    17 Choose 4

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

    What is 17 choose 4?

    Answer

    17 choose 4 is
    2,380

    Order doesn't matter, no repeats: 2,380 ways to choose 4 of 17 items.

    C(17, 4) = 17! / (4! · 13!)

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

    = 2,380

    If order matters (permutations): P(17, 4) = 17 × 16 × 15 × 14 = 57,120 — each combination in 4! = 24 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--4Copy
    <a href="https://calculat.io/en/number/combinations/17--4">17 Choose 4: Combinations C(17, 4) - Calculatio</a>Copy
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    17 Choose 4: Combinations C(17, 4). 17 choose 4 = 2,380: the number of ways to choose 4 of 17 items when order doesn't matter and nothing repeats. C(17, 4) = (17 × 16 × 15 × 14) / (4 × 3 × 2 × 1).
    https://calculat.io/en/number/combinations/17--4/generated.jpgCopy

    n choose 4 for other n

    n choose 4Answer
    7 choose 435
    8 choose 470
    9 choose 4126
    10 choose 4210
    11 choose 4330
    12 choose 4495
    13 choose 4715
    14 choose 41,001
    15 choose 41,365
    16 choose 41,820
    17 choose 42,380
    18 choose 43,060
    19 choose 43,876
    20 choose 44,845
    24 choose 410,626
    Recalculate with different values ↑

    FAQ

    What is 17 choose 4?

    17 choose 4 is 2,380

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

    Every way to choose 4 of 17 items leaves exactly 13 behind, so choosing 4 and choosing which 13 to leave out are the same count: 17 choose 4 = 17 choose 13 = 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, 4) = 57,120. Each of the 2,380 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also