Calculators & Converters

    9C6: 9 CHOOSE 6

    nCr - Combination Calculator

    9C6: 9 choose 6 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 6 elements at a time from 8 distinct elements without considering the order of elements.

    nCk of 9C6:
    9 CHOOSE 6 = 84
    where,
    9 is the total number of distinct elements (n),
    6 is the the number of elements drawn or choosen at a time (k),
    84 is the total number of possible combination (C).

    9C6 Points to Remember:

    • 9 CHOOSE 6 can also be denoted as 9C6.
    • Draw 6 out of 9 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
    • In 84 possible combinations, AB and BA are not considered as different events.
    • AB and BA considered as a single combination in 84 events.

    For values other than 9 choose 6, use this below tool:
    CHOOSE   

    How-to find nCk: 9 CHOOSE 6?

    9C6 is the type of nCr or nCk problem. The below 9 choose 6 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 6 elements at a time from 9 distinct elements without considering the order of elements.

    Solved Example: :
    what is 9 choose 6?

    step 1 Address the input parameters and observe what to be found:
    Input values:
    Total number of distinct elements (n) = 9
    The number of elements drawn at a time (k) = 6

    What to be found:
    Find the total number of possible combinations while choosing 6 elements at a time from 9 distinct elements without considering the order of elements.

    step 2 Find the factorial of 9:
    9! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9

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

    step 4 Find the factorial of difference between 9 and 6:
    (9 - 6)! = 3!
    3! = 1 x 2 x 3

    step 5 Apply the values of 9!, 6! and 3! in the nCk formula:
    nCk = n!/k! (n - k)!
    9C6 =9!/6! x 3!

    =1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9/(1 x 2 x 3 x 4 x 5 x 6) x (1 x 2 x 3)

    step 6 Simplify the above 9C6 equation:
    =1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9/(1 x 2 x 3 x 4 x 5 x 6) x (1 x 2 x 3)

    = 7 x 8 x 9/6
    = 504/6

    9C6 = 84

    Hence,
    9 choose 6 equals to 84

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