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    9 Choose 6

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

    What is 9 choose 6?

    Answer

    9 choose 6 is
    84

    Order doesn't matter, no repeats: 84 ways to choose 6 of 9 items.

    Choosing 6 of 9 is the same as leaving 3 out: C(9, 6) = C(9, 3).

    C(9, 6) = 9! / (6! · 3!)

    = C(9, 3)

    = (9 × 8 × 7) / (3 × 2 × 1)
    = 504 / 6

    = 84

    If order matters (permutations): P(9, 6) = 9 × 8 × 7 × 6 × 5 × 4 = 60,480 — each combination in 6! = 720 orders.

    Row 9 of Pascal's triangle
    k9 choose k
    01
    19
    236
    384
    4126
    5126
    684
    736
    89
    91

    Row sum: 29 = 512 — all subsets of 9 items.

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    https://calculat.io/en/number/combinations/9--6Copy
    <a href="https://calculat.io/en/number/combinations/9--6">9 Choose 6: Combinations C(9, 6) - Calculatio</a>Copy
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    9 Choose 6: Combinations C(9, 6). 9 choose 6 = 84: the number of ways to choose 6 of 9 items when order doesn't matter and nothing repeats. C(9, 6) = (9 × 8 × 7) / (3 × 2 × 1).
    https://calculat.io/en/number/combinations/9--6/generated.jpgCopy

    n choose 6 for other n

    n choose 6Answer
    6 choose 61
    7 choose 67
    8 choose 628
    9 choose 684
    10 choose 6210
    11 choose 6462
    12 choose 6924
    13 choose 61,716
    14 choose 63,003
    15 choose 65,005
    16 choose 68,008
    17 choose 612,376
    18 choose 618,564
    19 choose 627,132
    20 choose 638,760
    Recalculate with different values ↑

    FAQ

    What is 9 choose 6?

    9 choose 6 is 84

    Why is 9 choose 6 the same as 9 choose 3?

    Every way to choose 6 of 9 items leaves exactly 3 behind, so choosing 6 and choosing which 3 to leave out are the same count: 9 choose 6 = 9 choose 3 = 84. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(9, 6) = 60,480. Each of the 84 combinations can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also