Calculators & Converters

    10C4: 10 CHOOSE 4

    nCr - Combination Calculator

    10C4: 10 choose 4 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 4 elements at a time from 8 distinct elements without considering the order of elements.

    nCk of 10C4:
    10 CHOOSE 4 = 210
    where,
    10 is the total number of distinct elements (n),
    4 is the the number of elements drawn or choosen at a time (k),
    210 is the total number of possible combination (C).

    10C4 Points to Remember:

    • 10 CHOOSE 4 can also be denoted as 10C4.
    • Draw 4 out of 10 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
    • In 210 possible combinations, AB and BA are not considered as different events.
    • AB and BA considered as a single combination in 210 events.

    For values other than 10 choose 4, use this below tool:
    CHOOSE   

    How-to find nCk: 10 CHOOSE 4?

    10C4 is the type of nCr or nCk problem. The below 10 choose 4 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 4 elements at a time from 10 distinct elements without considering the order of elements.

    Solved Example: :
    what is 10 choose 4?

    step 1 Address the input parameters and observe what to be found:
    Input values:
    Total number of distinct elements (n) = 10
    The number of elements drawn at a time (k) = 4

    What to be found:
    Find the total number of possible combinations while choosing 4 elements at a time from 10 distinct elements without considering the order of elements.

    step 2 Find the factorial of 10:
    10! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10

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

    step 4 Find the factorial of difference between 10 and 4:
    (10 - 4)! = 6!
    6! = 1 x 2 x 3 x 4 x 5 x 6

    step 5 Apply the values of 10!, 4! and 6! in the nCk formula:
    nCk = n!/k! (n - k)!
    10C4 =10!/4! x 6!

    =1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10/(1 x 2 x 3 x 4) x (1 x 2 x 3 x 4 x 5 x 6)

    step 6 Simplify the above 10C4 equation:
    =1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10/(1 x 2 x 3 x 4) x (1 x 2 x 3 x 4 x 5 x 6)

    = 7 x 8 x 9 x 10/24
    = 5040/24

    10C4 = 210

    Hence,
    10 choose 4 equals to 210

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