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    10 Choose 8

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

    What is 10 choose 8?

    Answer

    10 choose 8 is
    45

    Order doesn't matter, no repeats: 45 ways to choose 8 of 10 items.

    Choosing 8 of 10 is the same as leaving 2 out: C(10, 8) = C(10, 2).

    C(10, 8) = 10! / (8! · 2!)

    = C(10, 2)

    = (10 × 9) / (2 × 1)
    = 90 / 2

    = 45

    If order matters (permutations): P(10, 8) = 10 × 9 × 8 × … × 3 = 1,814,400 — each combination in 8! = 40,320 orders.

    Row 10 of Pascal's triangle
    k10 choose k
    01
    110
    245
    3120
    4210
    5252
    6210
    7120
    845
    910
    101

    Row sum: 210 = 1,024 — all subsets of 10 items.

    See Also

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    https://calculat.io/en/number/combinations/10--8Copy
    <a href="https://calculat.io/en/number/combinations/10--8">10 Choose 8: Combinations C(10, 8) - Calculatio</a>Copy
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    10 Choose 8: Combinations C(10, 8). 10 choose 8 = 45: the number of ways to choose 8 of 10 items when order doesn't matter and nothing repeats. C(10, 8) = (10 × 9) / (2 × 1).
    https://calculat.io/en/number/combinations/10--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 10 choose 8?

    10 choose 8 is 45

    Why is 10 choose 8 the same as 10 choose 2?

    Every way to choose 8 of 10 items leaves exactly 2 behind, so choosing 8 and choosing which 2 to leave out are the same count: 10 choose 8 = 10 choose 2 = 45. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(10, 8) = 1,814,400. Each of the 45 combinations can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also