Calculators & Converters

    What is 11 CHOOSE 3 or Value of 11C3?

    nCr - Combination Calculator

    11 CHOOSE 3 = 165 possible combinations.
    165 is the total number of all possible combinations for choosing 3 elements at a time from 11 distinct elements without considering the order of elements in statistics & probability surveys or experiments. The number of combinations for sample space 11 CHOOSE 3 can also be written as 11C3 in the format of nCr or nCk.

    n CHOOSE knCkCombinations
    10 CHOOSE 210C245
    10 CHOOSE 310C3120
    10 CHOOSE 410C4210
    11 CHOOSE 211C255
    11 CHOOSE 311C3165
    11 CHOOSE 311C3165

    How to Find 11C3 or 11 CHOOSE 3?

    The below is the complete work with step by step calculation for 11 CHOOSE 3 may helpful for grade school students to learn how find all possible combinations of 11C3 for sample space S in the statistical experiment or to solve the combinations worksheet problems by just changing the corresponding input values of 11 CHOOSE 3 calculator.

    Workout :
    step 1 Address the formula, input parameters & values
    n = 11
    k = 3
    Find what is 11 CHOOSE 3?

    step 2 Substitute n and r values in below nCk formula

    nCk = n!/k! (n - k)!
    11 CHOOSE 3 =11!/3! (11 - 3)!

    step 3 Find the factorial for 11!, 3! & 8!, substitute the corresponding values in the below expression and simplify.

    11C3 = 11!/3! (8)!

    =1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11/(1 x 2 x 3) (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8)

    = 9 x 10 x 11/6
    = 990/6

    11C3 = 165

    165 total possible combinations for 11 CHOOSE 3

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