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    6 Choose 2

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

    What is 6 choose 2?

    Answer

    6 choose 2 is
    15

    Order doesn't matter, no repeats: 15 ways to choose 2 of 6 items.

    C(6, 2) = 6! / (2! · 4!)

    = (6 × 5) / (2 × 1)
    = 30 / 2

    = 15

    If order matters (permutations): P(6, 2) = 6 × 5 = 30 — each combination in 2! = 2 orders.

    Row 6 of Pascal's triangle
    k6 choose k
    01
    16
    215
    320
    415
    56
    61

    Row sum: 26 = 64 — all subsets of 6 items.

    See Also

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    https://calculat.io/en/number/combinations/6--2Copy
    <a href="https://calculat.io/en/number/combinations/6--2">6 Choose 2: Combinations C(6, 2) - Calculatio</a>Copy
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    6 Choose 2: Combinations C(6, 2). 6 choose 2 = 15: the number of ways to choose 2 of 6 items when order doesn't matter and nothing repeats. C(6, 2) = (6 × 5) / (2 × 1).
    https://calculat.io/en/number/combinations/6--2/generated.jpgCopy

    n choose 2 for other n

    n choose 2Answer
    1 choose 20
    2 choose 21
    3 choose 23
    4 choose 26
    5 choose 210
    6 choose 215
    7 choose 221
    8 choose 228
    9 choose 236
    10 choose 245
    11 choose 255
    12 choose 266
    13 choose 278
    14 choose 291
    15 choose 2105
    Recalculate with different values ↑

    FAQ

    What is 6 choose 2?

    6 choose 2 is 15

    Why is 6 choose 2 the same as 6 choose 4?

    Every way to choose 2 of 6 items leaves exactly 4 behind, so choosing 2 and choosing which 4 to leave out are the same count: 6 choose 2 = 6 choose 4 = 15. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(6, 2) = 30. Each of the 15 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also