Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    20 Choose 13

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

    What is 20 choose 13?

    Answer

    20 choose 13 is
    77,520

    Order doesn't matter, no repeats: 77,520 ways to choose 13 of 20 items.

    Choosing 13 of 20 is the same as leaving 7 out: C(20, 13) = C(20, 7).

    C(20, 13) = 20! / (13! · 7!)

    = C(20, 7)

    = (20 × 19 × 18 × … × 14) / (7 × 6 × 5 × … × 1)

    7 factors on top and bottom

    = 390,700,800 / 5,040

    = 77,520

    If order matters (permutations): P(20, 13) = 20 × 19 × 18 × … × 8 = 482,718,652,416,000 — each combination in 13! = 6,227,020,800 orders.

    Row 20 of Pascal's triangle
    k20 choose k
    01
    120
    2190
    31,140
    44,845
    515,504
    638,760
    777,520
    8125,970
    9167,960
    10184,756
    11167,960
    12125,970
    1377,520
    1438,760
    1515,504
    164,845
    171,140
    18190
    1920
    201

    Row sum: 220 = 1,048,576 — all subsets of 20 items.

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/combinations/20--13Copy
    <a href="https://calculat.io/en/number/combinations/20--13">20 Choose 13: Combinations C(20, 13) - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    20 Choose 13: Combinations C(20, 13). 20 choose 13 = 77,520: the number of ways to choose 13 of 20 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/20--13/generated.jpgCopy

    n choose 13 for other n

    n choose 13Answer
    13 choose 131
    14 choose 1314
    15 choose 13105
    16 choose 13560
    17 choose 132,380
    18 choose 138,568
    19 choose 1327,132
    20 choose 1377,520
    Recalculate with different values ↑

    FAQ

    What is 20 choose 13?

    20 choose 13 is 77,520

    Why is 20 choose 13 the same as 20 choose 7?

    Every way to choose 13 of 20 items leaves exactly 7 behind, so choosing 13 and choosing which 7 to leave out are the same count: 20 choose 13 = 20 choose 7 = 77,520. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(20, 13) = 482,718,652,416,000. Each of the 77,520 combinations can be put in order in 13! = 6,227,020,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also