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    13 Choose 5

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

    What is 13 choose 5?

    Answer

    13 choose 5 is
    1,287

    Order doesn't matter, no repeats: 1,287 ways to choose 5 of 13 items.

    C(13, 5) = 13! / (5! · 8!)

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

    = 1,287

    If order matters (permutations): P(13, 5) = 13 × 12 × 11 × 10 × 9 = 154,440 — each combination in 5! = 120 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--5Copy
    <a href="https://calculat.io/en/number/combinations/13--5">13 Choose 5: Combinations C(13, 5) - Calculatio</a>Copy
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    13 Choose 5: Combinations C(13, 5). 13 choose 5 = 1,287: the number of ways to choose 5 of 13 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/13--5/generated.jpgCopy

    n choose 5 for other n

    n choose 5Answer
    6 choose 56
    7 choose 521
    8 choose 556
    9 choose 5126
    10 choose 5252
    11 choose 5462
    12 choose 5792
    13 choose 51,287
    14 choose 52,002
    15 choose 53,003
    16 choose 54,368
    17 choose 56,188
    18 choose 58,568
    19 choose 511,628
    20 choose 515,504
    Recalculate with different values ↑

    FAQ

    What is 13 choose 5?

    13 choose 5 is 1,287

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

    Every way to choose 5 of 13 items leaves exactly 8 behind, so choosing 5 and choosing which 8 to leave out are the same count: 13 choose 5 = 13 choose 8 = 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, 5) = 154,440. Each of the 1,287 combinations can be put in order in 5! = 120 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also