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    9 Choose 7

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

    What is 9 choose 7?

    Answer

    9 choose 7 is
    36

    Order doesn't matter, no repeats: 36 ways to choose 7 of 9 items.

    Choosing 7 of 9 is the same as leaving 2 out: C(9, 7) = C(9, 2).

    C(9, 7) = 9! / (7! · 2!)

    = C(9, 2)

    = (9 × 8) / (2 × 1)
    = 72 / 2

    = 36

    If order matters (permutations): P(9, 7) = 9 × 8 × 7 × … × 3 = 181,440 — each combination in 7! = 5,040 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.

    See Also

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    https://calculat.io/en/number/combinations/9--7Copy
    <a href="https://calculat.io/en/number/combinations/9--7">9 Choose 7: Combinations C(9, 7) - Calculatio</a>Copy
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    9 Choose 7: Combinations C(9, 7). 9 choose 7 = 36: the number of ways to choose 7 of 9 items when order doesn't matter and nothing repeats. C(9, 7) = (9 × 8) / (2 × 1).
    https://calculat.io/en/number/combinations/9--7/generated.jpgCopy

    n choose 7 for other n

    n choose 7Answer
    7 choose 71
    8 choose 78
    9 choose 736
    10 choose 7120
    11 choose 7330
    12 choose 7792
    13 choose 71,716
    14 choose 73,432
    15 choose 76,435
    16 choose 711,440
    17 choose 719,448
    18 choose 731,824
    19 choose 750,388
    20 choose 777,520
    Recalculate with different values ↑

    FAQ

    What is 9 choose 7?

    9 choose 7 is 36

    Why is 9 choose 7 the same as 9 choose 2?

    Every way to choose 7 of 9 items leaves exactly 2 behind, so choosing 7 and choosing which 2 to leave out are the same count: 9 choose 7 = 9 choose 2 = 36. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(9, 7) = 181,440. Each of the 36 combinations can be put in order in 7! = 5,040 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also