Calculators & Converters

    7C3: 7 CHOOSE 3

    nCr - Combination Calculator

    7C3: 7 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 7C3:
    7 CHOOSE 3 = 35
    where,
    7 is the total number of distinct elements (n),
    3 is the the number of elements drawn or choosen at a time (k),
    35 is the total number of possible combination (C).

    7C3 Points to Remember:

    • 7 CHOOSE 3 can also be denoted as 7C3.
    • Draw 3 out of 7 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
    • In 35 possible combinations, AB and BA are not considered as different events.
    • AB and BA considered as a single combination in 35 events.

    For values other than 7 choose 3, use this below tool:
    CHOOSE   

    How-to find nCk: 7 CHOOSE 3?

    7C3 is the type of nCr or nCk problem. The below 7 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 7 distinct elements without considering the order of elements.

    Solved Example: :
    what is 7 choose 3?

    step 1 Address the input parameters and observe what to be found:
    Input values:
    Total number of distinct elements (n) = 7
    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 7 distinct elements without considering the order of elements.

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

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

    step 4 Find the factorial of difference between 7 and 3:
    (7 - 3)! = 4!
    4! = 1 x 2 x 3 x 4

    step 5 Apply the values of 7!, 3! and 4! in the nCk formula:
    nCk = n!/k! (n - k)!
    7C3 =7!/3! x 4!

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

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

    = 5 x 6 x 7/6
    = 210/6

    7C3 = 35

    Hence,
    7 choose 3 equals to 35

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