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    40 Choose 3

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

    What is 40 choose 3?

    Answer

    40 choose 3 is
    9,880

    Order doesn't matter, no repeats: 9,880 ways to choose 3 of 40 items.

    C(40, 3) = 40! / (3! · 37!)

    = (40 × 39 × 38) / (3 × 2 × 1)
    = 59,280 / 6

    = 9,880

    If order matters (permutations): P(40, 3) = 40 × 39 × 38 = 59,280 — each combination in 3! = 6 orders.

    Row 40 of Pascal's triangle
    k40 choose k
    01
    140
    2780
    39,880
    491,390
    5658,008
    63,838,380
    ……
    401

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    https://calculat.io/en/number/combinations/40--3Copy
    <a href="https://calculat.io/en/number/combinations/40--3">40 Choose 3: Combinations C(40, 3) - Calculatio</a>Copy
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    40 Choose 3: Combinations C(40, 3). 40 choose 3 = 9,880: the number of ways to choose 3 of 40 items when order doesn't matter and nothing repeats. C(40, 3) = (40 × 39 × 38) / (3 × 2 × 1).
    https://calculat.io/en/number/combinations/40--3/generated.jpgCopy

    n choose 3 for other n

    n choose 3Answer
    9 choose 384
    10 choose 3120
    11 choose 3165
    12 choose 3220
    13 choose 3286
    14 choose 3364
    15 choose 3455
    16 choose 3560
    17 choose 3680
    18 choose 3816
    19 choose 3969
    20 choose 31,140
    25 choose 32,300
    40 choose 39,880
    100 choose 3161,700
    Recalculate with different values ↑

    FAQ

    What is 40 choose 3?

    40 choose 3 is 9,880

    Why is 40 choose 3 the same as 40 choose 37?

    Every way to choose 3 of 40 items leaves exactly 37 behind, so choosing 3 and choosing which 37 to leave out are the same count: 40 choose 3 = 40 choose 37 = 9,880. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(40, 3) = 59,280. Each of the 9,880 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also