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    14 Choose 7

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

    What is 14 choose 7?

    Answer

    14 choose 7 is
    3,432

    Order doesn't matter, no repeats: 3,432 ways to choose 7 of 14 items.

    C(14, 7) = 14! / (7! · 7!)

    = (14 × 13 × 12 × … × 8) / (7 × 6 × 5 × … × 1)

    7 factors on top and bottom

    = 17,297,280 / 5,040

    = 3,432

    If order matters (permutations): P(14, 7) = 14 × 13 × 12 × … × 8 = 17,297,280 — each combination in 7! = 5,040 orders.

    Row 14 of Pascal's triangle
    k14 choose k
    01
    114
    291
    3364
    41,001
    52,002
    63,003
    73,432
    83,003
    92,002
    101,001
    11364
    1291
    1314
    141

    Row sum: 214 = 16,384 — all subsets of 14 items.

    See Also

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    https://calculat.io/en/number/combinations/14--7Copy
    <a href="https://calculat.io/en/number/combinations/14--7">14 Choose 7: Combinations C(14, 7) - Calculatio</a>Copy
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    14 Choose 7: Combinations C(14, 7). 14 choose 7 = 3,432: the number of ways to choose 7 of 14 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/14--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 14 choose 7?

    14 choose 7 is 3,432

    Why is 14 choose 7 the largest number in row 14?

    In row 14 of Pascal's triangle the numbers grow towards the middle and shrink after it, because n choose k = n choose (n − k). With an even n the middle is k = 7, so 14 choose 7 = 3,432 is the largest: 14 choose 6 is only 3,003.

    How many ways are there if order matters?

    P(14, 7) = 17,297,280. Each of the 3,432 combinations can be put in order in 7! = 5,040 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also