Calculators & Converters

    What is 10 CHOOSE 5 or Value of 10C5?

    nCr - Combination Calculator

    10 CHOOSE 5 = 252 possible combinations.
    252 is the total number of all possible combinations for choosing 5 elements at a time from 10 distinct elements without considering the order of elements in statistics & probability surveys or experiments. The number of combinations for sample space 10 CHOOSE 5 can also be written as 10C5 in the format of nCr or nCk.

    n CHOOSE knCkCombinations
    9 CHOOSE 49C4126
    9 CHOOSE 59C5126
    9 CHOOSE 69C684
    10 CHOOSE 410C4210
    10 CHOOSE 510C5252
    10 CHOOSE 510C5252

    How to Find 10C5 or 10 CHOOSE 5?

    The below is the complete work with step by step calculation for 10 CHOOSE 5 may helpful for grade school students to learn how find all possible combinations of 10C5 for sample space S in the statistical experiment or to solve the combinations worksheet problems by just changing the corresponding input values of 10 CHOOSE 5 calculator.

    Workout :
    step 1 Address the formula, input parameters & values
    n = 10
    k = 5
    Find what is 10 CHOOSE 5?

    step 2 Substitute n and r values in below nCk formula

    nCk = n!/k! (n - k)!
    10 CHOOSE 5 =10!/5! (10 - 5)!

    step 3 Find the factorial for 10!, 5! & 5!, substitute the corresponding values in the below expression and simplify.

    10C5 = 10!/5! (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) (1 x 2 x 3 x 4 x 5)

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

    10C5 = 252

    252 total possible combinations for 10 CHOOSE 5

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