Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    9 Choose 8

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

    What is 9 choose 8?

    Answer

    9 choose 8 is
    9

    Order doesn't matter, no repeats: 9 ways to choose 8 of 9 items.

    Choosing 8 of 9 is the same as leaving 1 out: C(9, 8) = C(9, 1).

    C(9, 8) = 9! / (8! · 1!)

    = C(9, 1)

    = 9 / 1

    = 9

    If order matters (permutations): P(9, 8) = 9 × 8 × 7 × … × 2 = 362,880 — each combination in 8! = 40,320 orders.

    Row 9 of Pascal's triangle
    k9 choose k
    01
    19
    236
    384
    4126
    5126
    684
    736
    89
    91

    Row sum: 29 = 512 — all subsets of 9 items.

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/combinations/9--8Copy
    <a href="https://calculat.io/en/number/combinations/9--8">9 Choose 8: Combinations C(9, 8) - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    9 Choose 8: Combinations C(9, 8). 9 choose 8 = 9: the number of ways to choose 8 of 9 items when order doesn't matter and nothing repeats. C(9, 8) = 9 / 1.
    https://calculat.io/en/number/combinations/9--8/generated.jpgCopy

    n choose 8 for other n

    n choose 8Answer
    8 choose 81
    9 choose 89
    10 choose 845
    11 choose 8165
    12 choose 8495
    13 choose 81,287
    14 choose 83,003
    15 choose 86,435
    16 choose 812,870
    17 choose 824,310
    18 choose 843,758
    19 choose 875,582
    20 choose 8125,970
    Recalculate with different values ↑

    FAQ

    What is 9 choose 8?

    9 choose 8 is 9

    Why is 9 choose 8 the same as 9 choose 1?

    Every way to choose 8 of 9 items leaves exactly 1 behind, so choosing 8 and choosing which one to leave out are the same count: 9 choose 8 = 9 choose 1 = 9. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

    How many ways are there if order matters?

    P(9, 8) = 362,880. Each of the 9 combinations can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

    See Also