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    13 Choose 8

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

    What is 13 choose 8?

    Answer

    13 choose 8 is
    1,287

    Order doesn't matter, no repeats: 1,287 ways to choose 8 of 13 items.

    Choosing 8 of 13 is the same as leaving 5 out: C(13, 8) = C(13, 5).

    C(13, 8) = 13! / (8! · 5!)

    = C(13, 5)

    = (13 × 12 × 11 × 10 × 9) / (5 × 4 × 3 × 2 × 1)
    = 154,440 / 120

    = 1,287

    If order matters (permutations): P(13, 8) = 13 × 12 × 11 × … × 6 = 51,891,840 — each combination in 8! = 40,320 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.

    See Also

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    https://calculat.io/en/number/combinations/13--8Copy
    <a href="https://calculat.io/en/number/combinations/13--8">13 Choose 8: Combinations C(13, 8) - Calculatio</a>Copy
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    13 Choose 8: Combinations C(13, 8). 13 choose 8 = 1,287: the number of ways to choose 8 of 13 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/13--8/generated.jpgCopy

    n choose 8 for other n

    n choose 8Answer
    8 choose 81
    9 choose 89
    10 choose 845
    11 choose 8165
    12 choose 8495
    13 choose 81,287
    14 choose 83,003
    15 choose 86,435
    16 choose 812,870
    17 choose 824,310
    18 choose 843,758
    19 choose 875,582
    20 choose 8125,970
    Recalculate with different values ↑

    FAQ

    What is 13 choose 8?

    13 choose 8 is 1,287

    Why is 13 choose 8 the same as 13 choose 5?

    Every way to choose 8 of 13 items leaves exactly 5 behind, so choosing 8 and choosing which 5 to leave out are the same count: 13 choose 8 = 13 choose 5 = 1,287. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(13, 8) = 51,891,840. Each of the 1,287 combinations can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also