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    11 Choose 3

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

    What is 11 choose 3?

    Answer

    11 choose 3 is
    165

    Order doesn't matter, no repeats: 165 ways to choose 3 of 11 items.

    C(11, 3) = 11! / (3! · 8!)

    = (11 × 10 × 9) / (3 × 2 × 1)
    = 990 / 6

    = 165

    If order matters (permutations): P(11, 3) = 11 × 10 × 9 = 990 — each combination in 3! = 6 orders.

    Row 11 of Pascal's triangle
    k11 choose k
    01
    111
    255
    3165
    4330
    5462
    6462
    7330
    8165
    955
    1011
    111

    Row sum: 211 = 2,048 — all subsets of 11 items.

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    https://calculat.io/en/number/combinations/11--3Copy
    <a href="https://calculat.io/en/number/combinations/11--3">11 Choose 3: Combinations C(11, 3) - Calculatio</a>Copy
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    11 Choose 3: Combinations C(11, 3). 11 choose 3 = 165: the number of ways to choose 3 of 11 items when order doesn't matter and nothing repeats. C(11, 3) = (11 × 10 × 9) / (3 × 2 × 1).
    https://calculat.io/en/number/combinations/11--3/generated.jpgCopy

    n choose 3 for other n

    n choose 3Answer
    4 choose 34
    5 choose 310
    6 choose 320
    7 choose 335
    8 choose 356
    9 choose 384
    10 choose 3120
    11 choose 3165
    12 choose 3220
    13 choose 3286
    14 choose 3364
    15 choose 3455
    16 choose 3560
    17 choose 3680
    18 choose 3816
    Recalculate with different values ↑

    FAQ

    What is 11 choose 3?

    11 choose 3 is 165

    Why is 11 choose 3 the same as 11 choose 8?

    Every way to choose 3 of 11 items leaves exactly 8 behind, so choosing 3 and choosing which 8 to leave out are the same count: 11 choose 3 = 11 choose 8 = 165. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(11, 3) = 990. Each of the 165 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also