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    13 Choose 10

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

    What is 13 choose 10?

    Answer

    13 choose 10 is
    286

    Order doesn't matter, no repeats: 286 ways to choose 10 of 13 items.

    Choosing 10 of 13 is the same as leaving 3 out: C(13, 10) = C(13, 3).

    C(13, 10) = 13! / (10! · 3!)

    = C(13, 3)

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

    = 286

    If order matters (permutations): P(13, 10) = 13 × 12 × 11 × … × 4 = 1,037,836,800 — each combination in 10! = 3,628,800 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--10Copy
    <a href="https://calculat.io/en/number/combinations/13--10">13 Choose 10: Combinations C(13, 10) - Calculatio</a>Copy
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    13 Choose 10: Combinations C(13, 10). 13 choose 10 = 286: the number of ways to choose 10 of 13 items when order doesn't matter and nothing repeats. C(13, 10) = (13 × 12 × 11) / (3 × 2 × 1).
    https://calculat.io/en/number/combinations/13--10/generated.jpgCopy

    n choose 10 for other n

    n choose 10Answer
    2 choose 100
    10 choose 101
    11 choose 1011
    12 choose 1066
    13 choose 10286
    14 choose 101,001
    15 choose 103,003
    16 choose 108,008
    17 choose 1019,448
    18 choose 1043,758
    19 choose 1092,378
    20 choose 10184,756
    100 choose 1017,310,309,456,440
    Recalculate with different values ↑

    FAQ

    What is 13 choose 10?

    13 choose 10 is 286

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

    Every way to choose 10 of 13 items leaves exactly 3 behind, so choosing 10 and choosing which 3 to leave out are the same count: 13 choose 10 = 13 choose 3 = 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, 10) = 1,037,836,800. Each of the 286 combinations can be put in order in 10! = 3,628,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also