Calculators & Converters

    3C1: 3 CHOOSE 1

    nCr - Combination Calculator

    3C1: 3 choose 1 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 1 elements at a time from 8 distinct elements without considering the order of elements.

    nCk of 3C1:
    3 CHOOSE 1 = 3
    where,
    3 is the total number of distinct elements (n),
    1 is the the number of elements drawn or choosen at a time (k),
    3 is the total number of possible combination (C).

    3C1 Points to Remember:

    • 3 CHOOSE 1 can also be denoted as 3C1.
    • Draw 1 out of 3 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
    • In 3 possible combinations, AB and BA are not considered as different events.
    • AB and BA considered as a single combination in 3 events.

    For values other than 3 choose 1, use this below tool:
    CHOOSE   

    How-to find nCk: 3 CHOOSE 1?

    3C1 is the type of nCr or nCk problem. The below 3 choose 1 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 1 elements at a time from 3 distinct elements without considering the order of elements.

    Solved Example: :
    what is 3 choose 1?

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

    What to be found:
    Find the total number of possible combinations while choosing 1 elements at a time from 3 distinct elements without considering the order of elements.

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

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

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

    step 5 Apply the values of 3!, 1! and 2! in the nCk formula:
    nCk = n!/k! (n - k)!
    3C1 =3!/1! x 2!

    =1 x 2 x 3/(1) x (1 x 2)

    step 6 Simplify the above 3C1 equation:
    =1 x 2 x 3/(1) x (1 x 2)

    Hence,
    3 choose 1 equals to 3

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