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    17 Choose 16

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

    What is 17 choose 16?

    Answer

    17 choose 16 is
    17

    Order doesn't matter, no repeats: 17 ways to choose 16 of 17 items.

    Choosing 16 of 17 is the same as leaving 1 out: C(17, 16) = C(17, 1).

    C(17, 16) = 17! / (16! · 1!)

    = C(17, 1)

    = 17 / 1

    = 17

    If order matters (permutations): P(17, 16) = 17 × 16 × 15 × … × 2 = 355,687,428,096,000 — each combination in 16! = 20,922,789,888,000 orders.

    Row 17 of Pascal's triangle
    k17 choose k
    01
    117
    2136
    3680
    42,380
    56,188
    612,376
    719,448
    824,310
    924,310
    1019,448
    1112,376
    126,188
    132,380
    14680
    15136
    1617
    171

    Row sum: 217 = 131,072 — all subsets of 17 items.

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    https://calculat.io/en/number/combinations/17--16Copy
    <a href="https://calculat.io/en/number/combinations/17--16">17 Choose 16: Combinations C(17, 16) - Calculatio</a>Copy
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    17 Choose 16: Combinations C(17, 16). 17 choose 16 = 17: the number of ways to choose 16 of 17 items when order doesn't matter and nothing repeats. C(17, 16) = 17 / 1.
    https://calculat.io/en/number/combinations/17--16/generated.jpgCopy

    n choose 16 for other n

    n choose 16Answer
    16 choose 161
    17 choose 1617
    18 choose 16153
    19 choose 16969
    20 choose 164,845
    Recalculate with different values ↑

    FAQ

    What is 17 choose 16?

    17 choose 16 is 17

    Why is 17 choose 16 the same as 17 choose 1?

    Every way to choose 16 of 17 items leaves exactly 1 behind, so choosing 16 and choosing which one to leave out are the same count: 17 choose 16 = 17 choose 1 = 17. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(17, 16) = 355,687,428,096,000. Each of the 17 combinations can be put in order in 16! = 20,922,789,888,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also