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    100 Choose 3

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

    What is 100 choose 3?

    Answer

    100 choose 3 is
    161,700

    Order doesn't matter, no repeats: 161,700 ways to choose 3 of 100 items.

    C(100, 3) = 100! / (3! · 97!)

    = (100 × 99 × 98) / (3 × 2 × 1)
    = 970,200 / 6

    = 161,700

    If order matters (permutations): P(100, 3) = 100 × 99 × 98 = 970,200 — each combination in 3! = 6 orders.

    Row 100 of Pascal's triangle
    k100 choose k
    01
    1100
    24,950
    3161,700
    43,921,225
    575,287,520
    61,192,052,400
    ……
    1001

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    https://calculat.io/en/number/combinations/100--3Copy
    <a href="https://calculat.io/en/number/combinations/100--3">100 Choose 3: Combinations C(100, 3) - Calculatio</a>Copy
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    100 Choose 3: Combinations C(100, 3). 100 choose 3 = 161,700: the number of ways to choose 3 of 100 items when order doesn't matter and nothing repeats. C(100, 3) = (100 × 99 × 98) / (3 × 2 × 1).
    https://calculat.io/en/number/combinations/100--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 100 choose 3?

    100 choose 3 is 161,700

    Why is 100 choose 3 the same as 100 choose 97?

    Every way to choose 3 of 100 items leaves exactly 97 behind, so choosing 3 and choosing which 97 to leave out are the same count: 100 choose 3 = 100 choose 97 = 161,700. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(100, 3) = 970,200. Each of the 161,700 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also