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    13 Choose 4

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

    What is 13 choose 4?

    Answer

    13 choose 4 is
    715

    Order doesn't matter, no repeats: 715 ways to choose 4 of 13 items.

    C(13, 4) = 13! / (4! · 9!)

    = (13 × 12 × 11 × 10) / (4 × 3 × 2 × 1)
    = 17,160 / 24

    = 715

    If order matters (permutations): P(13, 4) = 13 × 12 × 11 × 10 = 17,160 — each combination in 4! = 24 orders.

    Row 13 of Pascal's triangle
    k13 choose k
    01
    113
    278
    3286
    4715
    51,287
    61,716
    71,716
    81,287
    9715
    10286
    1178
    1213
    131

    Row sum: 213 = 8,192 — all subsets of 13 items.

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    https://calculat.io/en/number/combinations/13--4Copy
    <a href="https://calculat.io/en/number/combinations/13--4">13 Choose 4: Combinations C(13, 4) - Calculatio</a>Copy
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    13 Choose 4: Combinations C(13, 4). 13 choose 4 = 715: the number of ways to choose 4 of 13 items when order doesn't matter and nothing repeats. C(13, 4) = (13 × 12 × 11 × 10) / (4 × 3 × 2 × 1).
    https://calculat.io/en/number/combinations/13--4/generated.jpgCopy

    n choose 4 for other n

    n choose 4Answer
    6 choose 415
    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
    Recalculate with different values ↑

    FAQ

    What is 13 choose 4?

    13 choose 4 is 715

    Why is 13 choose 4 the same as 13 choose 9?

    Every way to choose 4 of 13 items leaves exactly 9 behind, so choosing 4 and choosing which 9 to leave out are the same count: 13 choose 4 = 13 choose 9 = 715. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(13, 4) = 17,160. Each of the 715 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also