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    100 Choose 10

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

    What is 100 choose 10?

    Answer

    100 choose 10 is
    17,310,309,456,440

    Order doesn't matter, no repeats: 17,310,309,456,440 ways to choose 10 of 100 items.

    C(100, 10) = 100! / (10! · 90!)

    = (100 × 99 × 98 × … × 91) / (10 × 9 × 8 × … × 1)

    10 factors on top and bottom

    = 62,815,650,955,529,472,000 / 3,628,800

    = 17,310,309,456,440

    If order matters (permutations): P(100, 10) = 100 × 99 × 98 × … × 91 = 62,815,650,955,529,472,000 — each combination in 10! = 3,628,800 orders.

    Row 100 of Pascal's triangle
    k100 choose k
    01
    ……
    716,007,560,800
    8186,087,894,300
    91,902,231,808,400
    1017,310,309,456,440
    11141,629,804,643,600
    121,050,421,051,106,700
    137,110,542,499,799,200
    ……
    1001

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    https://calculat.io/en/number/combinations/100--10Copy
    <a href="https://calculat.io/en/number/combinations/100--10">100 Choose 10: Combinations C(100, 10) - Calculatio</a>Copy
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    100 Choose 10: Combinations C(100, 10). 100 choose 10 = 17,310,309,456,440: the number of ways to choose 10 of 100 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/100--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 100 choose 10?

    100 choose 10 is 17,310,309,456,440

    Why is 100 choose 10 the same as 100 choose 90?

    Every way to choose 10 of 100 items leaves exactly 90 behind, so choosing 10 and choosing which 90 to leave out are the same count: 100 choose 10 = 100 choose 90 = 17,310,309,456,440. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(100, 10) = 62,815,650,955,529,472,000. Each of the 17,310,309,456,440 combinations can be put in order in 10! = 3,628,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also