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    25 Choose 3

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

    What is 25 choose 3?

    Answer

    25 choose 3 is
    2,300

    Order doesn't matter, no repeats: 2,300 ways to choose 3 of 25 items.

    C(25, 3) = 25! / (3! · 22!)

    = (25 × 24 × 23) / (3 × 2 × 1)
    = 13,800 / 6

    = 2,300

    If order matters (permutations): P(25, 3) = 25 × 24 × 23 = 13,800 — each combination in 3! = 6 orders.

    Row 25 of Pascal's triangle
    k25 choose k
    01
    125
    2300
    32,300
    412,650
    553,130
    6177,100
    ……
    251

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    https://calculat.io/en/number/combinations/25--3Copy
    <a href="https://calculat.io/en/number/combinations/25--3">25 Choose 3: Combinations C(25, 3) - Calculatio</a>Copy
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    25 Choose 3: Combinations C(25, 3). 25 choose 3 = 2,300: the number of ways to choose 3 of 25 items when order doesn't matter and nothing repeats. C(25, 3) = (25 × 24 × 23) / (3 × 2 × 1).
    https://calculat.io/en/number/combinations/25--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 25 choose 3?

    25 choose 3 is 2,300

    Why is 25 choose 3 the same as 25 choose 22?

    Every way to choose 3 of 25 items leaves exactly 22 behind, so choosing 3 and choosing which 22 to leave out are the same count: 25 choose 3 = 25 choose 22 = 2,300. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(25, 3) = 13,800. Each of the 2,300 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also