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    11 Choose 5

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

    What is 11 choose 5?

    Answer

    11 choose 5 is
    462

    Order doesn't matter, no repeats: 462 ways to choose 5 of 11 items.

    C(11, 5) = 11! / (5! · 6!)

    = (11 × 10 × 9 × 8 × 7) / (5 × 4 × 3 × 2 × 1)
    = 55,440 / 120

    = 462

    If order matters (permutations): P(11, 5) = 11 × 10 × 9 × 8 × 7 = 55,440 — each combination in 5! = 120 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--5Copy
    <a href="https://calculat.io/en/number/combinations/11--5">11 Choose 5: Combinations C(11, 5) - Calculatio</a>Copy
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    11 Choose 5: Combinations C(11, 5). 11 choose 5 = 462: the number of ways to choose 5 of 11 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/11--5/generated.jpgCopy

    n choose 5 for other n

    n choose 5Answer
    2 choose 50
    5 choose 51
    6 choose 56
    7 choose 521
    8 choose 556
    9 choose 5126
    10 choose 5252
    11 choose 5462
    12 choose 5792
    13 choose 51,287
    14 choose 52,002
    15 choose 53,003
    16 choose 54,368
    17 choose 56,188
    18 choose 58,568
    Recalculate with different values ↑

    FAQ

    What is 11 choose 5?

    11 choose 5 is 462

    Why is 11 choose 5 the same as 11 choose 6?

    Every way to choose 5 of 11 items leaves exactly 6 behind, so choosing 5 and choosing which 6 to leave out are the same count: 11 choose 5 = 11 choose 6 = 462. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(11, 5) = 55,440. Each of the 462 combinations can be put in order in 5! = 120 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also