Calculators & Converters

    8C3: 8 CHOOSE 3

    nCr - Combination Calculator

    8C3: 8 choose 3 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 3 elements at a time from 8 distinct elements without considering the order of elements.

    nCk of 8C3:
    8 CHOOSE 3 = 56
    where,
    8 is the total number of distinct elements (n),
    3 is the the number of elements drawn or choosen at a time (k),
    56 is the total number of possible combination (C).

    8C3 Points to Remember:

    • 8 CHOOSE 3 can also be denoted as 8C3.
    • Draw 3 out of 8 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
    • In 56 possible combinations, AB and BA are not considered as different events.
    • AB and BA considered as a single combination in 56 events.

    For values other than 8 choose 3, use this below tool:
    CHOOSE   

    How-to find nCk: 8 CHOOSE 3?

    8C3 is the type of nCr or nCk problem. The below 8 choose 3 work with steps help users to understand the combinations nCk formula, input parameters and how to find how many possible combinations/events occur while drawing 3 elements at a time from 8 distinct elements without considering the order of elements.

    Solved Example: :
    what is 8 choose 3?

    step 1 Address the input parameters and observe what to be found:
    Input values:
    Total number of distinct elements (n) = 8
    The number of elements drawn at a time (k) = 3

    What to be found:
    Find the total number of possible combinations while choosing 3 elements at a time from 8 distinct elements without considering the order of elements.

    step 2 Find the factorial of 8:
    8! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8

    step 3 Find the factorial of 3:
    3! = 1 x 2 x 3

    step 4 Find the factorial of difference between 8 and 3:
    (8 - 3)! = 5!
    5! = 1 x 2 x 3 x 4 x 5

    step 5 Apply the values of 8!, 3! and 5! in the nCk formula:
    nCk = n!/k! (n - k)!
    8C3 =8!/3! x 5!

    =1 x 2 x 3 x 4 x 5 x 6 x 7 x 8/(1 x 2 x 3) x (1 x 2 x 3 x 4 x 5)

    step 6 Simplify the above 8C3 equation:
    =1 x 2 x 3 x 4 x 5 x 6 x 7 x 8/(1 x 2 x 3) x (1 x 2 x 3 x 4 x 5)

    = 6 x 7 x 8/6
    = 336/6

    8C3 = 56

    Hence,
    8 choose 3 equals to 56

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