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    20 Choose 10

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

    What is 20 choose 10?

    Answer

    20 choose 10 is
    184,756

    Order doesn't matter, no repeats: 184,756 ways to choose 10 of 20 items.

    C(20, 10) = 20! / (10! · 10!)

    = (20 × 19 × 18 × … × 11) / (10 × 9 × 8 × … × 1)

    10 factors on top and bottom

    = 670,442,572,800 / 3,628,800

    = 184,756

    If order matters (permutations): P(20, 10) = 20 × 19 × 18 × … × 11 = 670,442,572,800 — each combination in 10! = 3,628,800 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

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    https://calculat.io/en/number/combinations/20--10Copy
    <a href="https://calculat.io/en/number/combinations/20--10">20 Choose 10: Combinations C(20, 10) - Calculatio</a>Copy
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    20 Choose 10: Combinations C(20, 10). 20 choose 10 = 184,756: the number of ways to choose 10 of 20 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/20--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 20 choose 10?

    20 choose 10 is 184,756

    Why is 20 choose 10 the largest number in row 20?

    In row 20 of Pascal's triangle the numbers grow towards the middle and shrink after it, because n choose k = n choose (n − k). With an even n the middle is k = 10, so 20 choose 10 = 184,756 is the largest: 20 choose 9 is only 167,960.

    How many ways are there if order matters?

    P(20, 10) = 670,442,572,800. Each of the 184,756 combinations can be put in order in 10! = 3,628,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also