Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    16 Choose 14

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

    What is 16 choose 14?

    Answer

    16 choose 14 is
    120

    Order doesn't matter, no repeats: 120 ways to choose 14 of 16 items.

    Choosing 14 of 16 is the same as leaving 2 out: C(16, 14) = C(16, 2).

    C(16, 14) = 16! / (14! · 2!)

    = C(16, 2)

    = (16 × 15) / (2 × 1)
    = 240 / 2

    = 120

    If order matters (permutations): P(16, 14) = 16 × 15 × 14 × … × 3 = 10,461,394,944,000 — each combination in 14! = 87,178,291,200 orders.

    Row 16 of Pascal's triangle
    k16 choose k
    01
    116
    2120
    3560
    41,820
    54,368
    68,008
    711,440
    812,870
    911,440
    108,008
    114,368
    121,820
    13560
    14120
    1516
    161

    Row sum: 216 = 65,536 — all subsets of 16 items.

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/combinations/16--14Copy
    <a href="https://calculat.io/en/number/combinations/16--14">16 Choose 14: Combinations C(16, 14) - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    16 Choose 14: Combinations C(16, 14). 16 choose 14 = 120: the number of ways to choose 14 of 16 items when order doesn't matter and nothing repeats. C(16, 14) = (16 × 15) / (2 × 1).
    https://calculat.io/en/number/combinations/16--14/generated.jpgCopy

    n choose 14 for other n

    n choose 14Answer
    14 choose 141
    15 choose 1415
    16 choose 14120
    17 choose 14680
    18 choose 143,060
    19 choose 1411,628
    20 choose 1438,760
    Recalculate with different values ↑

    FAQ

    What is 16 choose 14?

    16 choose 14 is 120

    Why is 16 choose 14 the same as 16 choose 2?

    Every way to choose 14 of 16 items leaves exactly 2 behind, so choosing 14 and choosing which 2 to leave out are the same count: 16 choose 14 = 16 choose 2 = 120. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(16, 14) = 10,461,394,944,000. Each of the 120 combinations can be put in order in 14! = 87,178,291,200 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also