Calculators & Converters

    What is 17 CHOOSE 3 or Value of 17C3?

    nCr - Combination Calculator

    17 CHOOSE 3 = 680 possible combinations.
    680 is the total number of all possible combinations for choosing 3 elements at a time from 17 distinct elements without considering the order of elements in statistics & probability surveys or experiments. The number of combinations for sample space 17 CHOOSE 3 can also be written as 17C3 in the format of nCr or nCk.

    n CHOOSE knCkCombinations
    11 CHOOSE 211C255
    11 CHOOSE 311C3165
    11 CHOOSE 411C4330
    12 CHOOSE 212C266
    12 CHOOSE 312C3220

    How to Find 17C3 or 17 CHOOSE 3?

    The below is the complete work with step by step calculation for 17 CHOOSE 3 may helpful for grade school students to learn how find all possible combinations of 17C3 for sample space S in the statistical experiment or to solve the combinations worksheet problems by just changing the corresponding input values of 17 CHOOSE 3 calculator.

    Workout :
    step 1 Address the formula, input parameters & values
    n = 17
    k = 3
    Find what is 17 CHOOSE 3?

    step 2 Substitute n and r values in below nCk formula

    nCk = n!/k! (n - k)!
    17 CHOOSE 3 =17!/3! (17 - 3)!

    step 3 Find the factorial for 17!, 3! & 14!, substitute the corresponding values in the below expression and simplify.

    17C3 = 17!/3! (14)!

    =1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15 x 16 x 17/(1 x 2 x 3) (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14)

    = 15 x 16 x 17/6
    = 4080/6

    17C3 = 680

    680 total possible combinations for 17 CHOOSE 3

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