Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    14 Choose 5

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

    What is 14 choose 5?

    Answer

    14 choose 5 is
    2,002

    Order doesn't matter, no repeats: 2,002 ways to choose 5 of 14 items.

    C(14, 5) = 14! / (5! · 9!)

    = (14 × 13 × 12 × 11 × 10) / (5 × 4 × 3 × 2 × 1)
    = 240,240 / 120

    = 2,002

    If order matters (permutations): P(14, 5) = 14 × 13 × 12 × 11 × 10 = 240,240 — each combination in 5! = 120 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

    Share This Calculation
    Print
    https://calculat.io/en/number/combinations/14--5Copy
    <a href="https://calculat.io/en/number/combinations/14--5">14 Choose 5: Combinations C(14, 5) - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    14 Choose 5: Combinations C(14, 5). 14 choose 5 = 2,002: the number of ways to choose 5 of 14 items when order doesn't matter and nothing repeats.
    https://calculat.io/en/number/combinations/14--5/generated.jpgCopy

    n choose 5 for other n

    n choose 5Answer
    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
    19 choose 511,628
    20 choose 515,504
    Recalculate with different values ↑

    FAQ

    What is 14 choose 5?

    14 choose 5 is 2,002

    Why is 14 choose 5 the same as 14 choose 9?

    Every way to choose 5 of 14 items leaves exactly 9 behind, so choosing 5 and choosing which 9 to leave out are the same count: 14 choose 5 = 14 choose 9 = 2,002. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(14, 5) = 240,240. Each of the 2,002 combinations can be put in order in 5! = 120 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also