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    10 Choose 4

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

    What is 10 choose 4?

    Answer

    10 choose 4 is
    210

    Order doesn't matter, no repeats: 210 ways to choose 4 of 10 items.

    C(10, 4) = 10! / (4! · 6!)

    = (10 × 9 × 8 × 7) / (4 × 3 × 2 × 1)
    = 5,040 / 24

    = 210

    If order matters (permutations): P(10, 4) = 10 × 9 × 8 × 7 = 5,040 — each combination in 4! = 24 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.

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    https://calculat.io/en/number/combinations/10--4Copy
    <a href="https://calculat.io/en/number/combinations/10--4">10 Choose 4: Combinations C(10, 4) - Calculatio</a>Copy
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    10 Choose 4: Combinations C(10, 4). 10 choose 4 = 210: the number of ways to choose 4 of 10 items when order doesn't matter and nothing repeats. C(10, 4) = (10 × 9 × 8 × 7) / (4 × 3 × 2 × 1).
    https://calculat.io/en/number/combinations/10--4/generated.jpgCopy

    n choose 4 for other n

    n choose 4Answer
    3 choose 40
    4 choose 41
    5 choose 45
    6 choose 415
    7 choose 435
    8 choose 470
    9 choose 4126
    10 choose 4210
    11 choose 4330
    12 choose 4495
    13 choose 4715
    14 choose 41,001
    15 choose 41,365
    16 choose 41,820
    17 choose 42,380
    Recalculate with different values ↑

    FAQ

    What is 10 choose 4?

    10 choose 4 is 210

    Why is 10 choose 4 the same as 10 choose 6?

    Every way to choose 4 of 10 items leaves exactly 6 behind, so choosing 4 and choosing which 6 to leave out are the same count: 10 choose 4 = 10 choose 6 = 210. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(10, 4) = 5,040. Each of the 210 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also