Calculators & Converters

    What is 52 CHOOSE 5 or Value of 52C5?

    nCr - Combination Calculator

    52 CHOOSE 5 = 2598960 possible combinations.
    2598960 is the total number of all possible combinations for choosing 5 elements at a time from 52 distinct elements without considering the order of elements in statistics & probability surveys or experiments. The number of combinations for sample space 52 CHOOSE 5 can also be written as 52C5 in the format of nCr or nCk.

    n CHOOSE knCkCombinations
    11 CHOOSE 411C4330
    11 CHOOSE 511C5462
    11 CHOOSE 611C6462
    12 CHOOSE 412C4495
    12 CHOOSE 512C5792

    How to Find 52C5 or 52 CHOOSE 5?

    The below is the complete work with step by step calculation for 52 CHOOSE 5 may helpful for grade school students to learn how find all possible combinations of 52C5 for sample space S in the statistical experiment or to solve the combinations worksheet problems by just changing the corresponding input values of 52 CHOOSE 5 calculator.

    Workout :
    step 1 Address the formula, input parameters & values
    n = 52
    k = 5
    Find what is 52 CHOOSE 5?

    step 2 Substitute n and r values in below nCk formula

    nCk = n!/k! (n - k)!
    52 CHOOSE 5 =52!/5! (52 - 5)!

    step 3 Find the factorial for 52!, 5! & 47!, substitute the corresponding values in the below expression and simplify.

    52C5 = 52!/5! (47)!

    =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 x 18 x 19 x 20 x 21 x 22 x 23 x 24 x 25 x 26 x 27 x 28 x 29 x 30 x 31 x 32 x 33 x 34 x 35 x 36 x 37 x 38 x 39 x 40 x 41 x 42 x 43 x 44 x 45 x 46 x 47 x 48 x 49 x 50 x 51 x 52/(1 x 2 x 3 x 4 x 5) (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 x 18 x 19 x 20 x 21 x 22 x 23 x 24 x 25 x 26 x 27 x 28 x 29 x 30 x 31 x 32 x 33 x 34 x 35 x 36 x 37 x 38 x 39 x 40 x 41 x 42 x 43 x 44 x 45 x 46 x 47)

    = 48 x 49 x 50 x 51 x 52/120
    = 311875200/120

    52C5 = 2598960

    2598960 total possible combinations for 52 CHOOSE 5

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