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    5 Choose 3

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

    What is 5 choose 3?

    Answer

    5 choose 3 is
    10

    Order doesn't matter, no repeats: 10 ways to choose 3 of 5 items.

    Choosing 3 of 5 is the same as leaving 2 out: C(5, 3) = C(5, 2).

    C(5, 3) = 5! / (3! · 2!)

    = C(5, 2)

    = (5 × 4) / (2 × 1)
    = 20 / 2

    = 10

    If order matters (permutations): P(5, 3) = 5 × 4 × 3 = 60 — each combination in 3! = 6 orders.

    Row 5 of Pascal's triangle
    k5 choose k
    01
    15
    210
    310
    45
    51

    Row sum: 25 = 32 — all subsets of 5 items.

    See Also

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    https://calculat.io/en/number/combinations/5--3Copy
    <a href="https://calculat.io/en/number/combinations/5--3">5 Choose 3: Combinations C(5, 3) - Calculatio</a>Copy
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    5 Choose 3: Combinations C(5, 3). 5 choose 3 = 10: the number of ways to choose 3 of 5 items when order doesn't matter and nothing repeats. C(5, 3) = (5 × 4) / (2 × 1).
    https://calculat.io/en/number/combinations/5--3/generated.jpgCopy

    n choose 3 for other n

    n choose 3Answer
    1 choose 30
    2 choose 30
    3 choose 31
    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
    Recalculate with different values ↑

    FAQ

    What is 5 choose 3?

    5 choose 3 is 10

    Why is 5 choose 3 the same as 5 choose 2?

    Every way to choose 3 of 5 items leaves exactly 2 behind, so choosing 3 and choosing which 2 to leave out are the same count: 5 choose 3 = 5 choose 2 = 10. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(5, 3) = 60. Each of the 10 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also