Calculators & Converters

    10C5: 10 CHOOSE 5

    nCr - Combination Calculator

    10C5: 10 choose 5 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 5 elements at a time from 8 distinct elements without considering the order of elements.

    nCk of 10C5:
    10 CHOOSE 5 = 252
    where,
    10 is the total number of distinct elements (n),
    5 is the the number of elements drawn or choosen at a time (k),
    252 is the total number of possible combination (C).

    10C5 Points to Remember:

    • 10 CHOOSE 5 can also be denoted as 10C5.
    • Draw 5 out of 10 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
    • In 252 possible combinations, AB and BA are not considered as different events.
    • AB and BA considered as a single combination in 252 events.

    For values other than 10 choose 5, use this below tool:
    CHOOSE   

    How-to find nCk: 10 CHOOSE 5?

    10C5 is the type of nCr or nCk problem. The below 10 choose 5 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 5 elements at a time from 10 distinct elements without considering the order of elements.

    Solved Example: :
    what is 10 choose 5?

    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) = 5

    What to be found:
    Find the total number of possible combinations while choosing 5 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 5:
    5! = 1 x 2 x 3 x 4 x 5

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

    step 5 Apply the values of 10!, 5! and 5! in the nCk formula:
    nCk = n!/k! (n - k)!
    10C5 =10!/5! x 5!

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

    step 6 Simplify the above 10C5 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 5) x (1 x 2 x 3 x 4 x 5)

    = 6 x 7 x 8 x 9 x 10/120
    = 30240/120

    10C5 = 252

    Hence,
    10 choose 5 equals to 252

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