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    13 Choose 3

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

    What is 13 choose 3?

    Answer

    13 choose 3 is
    286

    Order doesn't matter, no repeats: 286 ways to choose 3 of 13 items.

    C(13, 3) = 13! / (3! · 10!)

    = (13 × 12 × 11) / (3 × 2 × 1)
    = 1,716 / 6

    = 286

    If order matters (permutations): P(13, 3) = 13 × 12 × 11 = 1,716 — each combination in 3! = 6 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--3Copy
    <a href="https://calculat.io/en/number/combinations/13--3">13 Choose 3: Combinations C(13, 3) - Calculatio</a>Copy
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    13 Choose 3: Combinations C(13, 3). 13 choose 3 = 286: the number of ways to choose 3 of 13 items when order doesn't matter and nothing repeats. C(13, 3) = (13 × 12 × 11) / (3 × 2 × 1).
    https://calculat.io/en/number/combinations/13--3/generated.jpgCopy

    n choose 3 for other n

    n choose 3Answer
    6 choose 320
    7 choose 335
    8 choose 356
    9 choose 384
    10 choose 3120
    11 choose 3165
    12 choose 3220
    13 choose 3286
    14 choose 3364
    15 choose 3455
    16 choose 3560
    17 choose 3680
    18 choose 3816
    19 choose 3969
    20 choose 31,140
    Recalculate with different values ↑

    FAQ

    What is 13 choose 3?

    13 choose 3 is 286

    Why is 13 choose 3 the same as 13 choose 10?

    Every way to choose 3 of 13 items leaves exactly 10 behind, so choosing 3 and choosing which 10 to leave out are the same count: 13 choose 3 = 13 choose 10 = 286. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(13, 3) = 1,716. Each of the 286 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also