Calculators & Converters

    5C2: 5 CHOOSE 2

    nCr - Combination Calculator

    5C2: 5 choose 2 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 2 elements at a time from 8 distinct elements without considering the order of elements.

    nCk of 5C2:
    5 CHOOSE 2 = 10
    where,
    5 is the total number of distinct elements (n),
    2 is the the number of elements drawn or choosen at a time (k),
    10 is the total number of possible combination (C).

    5C2 Points to Remember:

    • 5 CHOOSE 2 can also be denoted as 5C2.
    • Draw 2 out of 5 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
    • In 10 possible combinations, AB and BA are not considered as different events.
    • AB and BA considered as a single combination in 10 events.

    For values other than 5 choose 2, use this below tool:
    CHOOSE   

    How-to find nCk: 5 CHOOSE 2?

    5C2 is the type of nCr or nCk problem. The below 5 choose 2 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 2 elements at a time from 5 distinct elements without considering the order of elements.

    Solved Example: :
    what is 5 choose 2?

    step 1 Address the input parameters and observe what to be found:
    Input values:
    Total number of distinct elements (n) = 5
    The number of elements drawn at a time (k) = 2

    What to be found:
    Find the total number of possible combinations while choosing 2 elements at a time from 5 distinct elements without considering the order of elements.

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

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

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

    step 5 Apply the values of 5!, 2! and 3! in the nCk formula:
    nCk = n!/k! (n - k)!
    5C2 =5!/2! x 3!

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

    step 6 Simplify the above 5C2 equation:
    =1 x 2 x 3 x 4 x 5/(1 x 2) x (1 x 2 x 3)

    = 4 x 5/2
    = 20/2

    5C2 = 10

    Hence,
    5 choose 2 equals to 10

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