Calculators & Converters

    6C3: 6 CHOOSE 3

    nCr - Combination Calculator

    6C3: 6 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 6C3:
    6 CHOOSE 3 = 20
    where,
    6 is the total number of distinct elements (n),
    3 is the the number of elements drawn or choosen at a time (k),
    20 is the total number of possible combination (C).

    6C3 Points to Remember:

    • 6 CHOOSE 3 can also be denoted as 6C3.
    • Draw 3 out of 6 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
    • In 20 possible combinations, AB and BA are not considered as different events.
    • AB and BA considered as a single combination in 20 events.

    For values other than 6 choose 3, use this below tool:
    CHOOSE   

    How-to find nCk: 6 CHOOSE 3?

    6C3 is the type of nCr or nCk problem. The below 6 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 6 distinct elements without considering the order of elements.

    Solved Example: :
    what is 6 choose 3?

    step 1 Address the input parameters and observe what to be found:
    Input values:
    Total number of distinct elements (n) = 6
    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 6 distinct elements without considering the order of elements.

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

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

    step 4 Find the factorial of difference between 6 and 3:
    (6 - 3)! = 3!
    3! = 1 x 2 x 3

    step 5 Apply the values of 6!, 3! and 3! in the nCk formula:
    nCk = n!/k! (n - k)!
    6C3 =6!/3! x 3!

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

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

    = 4 x 5 x 6/6
    = 120/6

    6C3 = 20

    Hence,
    6 choose 3 equals to 20

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