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    7 Choose 5

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

    What is 7 choose 5?

    Answer

    7 choose 5 is
    21

    Order doesn't matter, no repeats: 21 ways to choose 5 of 7 items.

    Choosing 5 of 7 is the same as leaving 2 out: C(7, 5) = C(7, 2).

    C(7, 5) = 7! / (5! · 2!)

    = C(7, 2)

    = (7 × 6) / (2 × 1)
    = 42 / 2

    = 21

    If order matters (permutations): P(7, 5) = 7 × 6 × 5 × 4 × 3 = 2,520 — each combination in 5! = 120 orders.

    Row 7 of Pascal's triangle
    k7 choose k
    01
    17
    221
    335
    435
    521
    67
    71

    Row sum: 27 = 128 — all subsets of 7 items.

    See Also

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    https://calculat.io/en/number/combinations/7--5Copy
    <a href="https://calculat.io/en/number/combinations/7--5">7 Choose 5: Combinations C(7, 5) - Calculatio</a>Copy
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    7 Choose 5: Combinations C(7, 5). 7 choose 5 = 21: the number of ways to choose 5 of 7 items when order doesn't matter and nothing repeats. C(7, 5) = (7 × 6) / (2 × 1).
    https://calculat.io/en/number/combinations/7--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 7 choose 5?

    7 choose 5 is 21

    Why is 7 choose 5 the same as 7 choose 2?

    Every way to choose 5 of 7 items leaves exactly 2 behind, so choosing 5 and choosing which 2 to leave out are the same count: 7 choose 5 = 7 choose 2 = 21. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(7, 5) = 2,520. Each of the 21 combinations can be put in order in 5! = 120 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also