52C13: 52 CHOOSE 13
52C13: 52 choose 13 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 13 elements at a time from 8 distinct elements without considering the order of elements.
nCk of 52C13:
52 CHOOSE 13 = 635013559600
where,
52 is the total number of distinct elements (n),
13 is the the number of elements drawn or choosen at a time (k),
635013559600 is the total number of possible combination (C).
52C13 Points to Remember:
- 52 CHOOSE 13 can also be denoted as 52C13.
- Draw 13 out of 52 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
- In 635013559600 possible combinations, AB and BA are not considered as different events.
- AB and BA considered as a single combination in 635013559600 events.
How-to find nCk: 52 CHOOSE 13?
52C13 is the type of nCr or nCk problem. The below 52 choose 13 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 13 elements at a time from 52 distinct elements without considering the order of elements.
Solved Example: :
what is 52 choose 13?
step 1 Address the input parameters and observe what to be found:
Input values:
Total number of distinct elements (n) = 52
The number of elements drawn at a time (k) = 13
What to be found:
Find the total number of possible combinations while choosing 13 elements at a time from 52 distinct elements without considering the order of elements.
step 2 Find the factorial of 52:
52! = 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
step 3 Find the factorial of 13:
13! = 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
step 4 Find the factorial of difference between 52 and 13:
(52 - 13)! = 39!
39! = 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
step 5 Apply the values of 52!, 13! and 39! in the nCk formula:
nCk = n!/k! (n - k)!
52C13 =52!/13! x 39!
=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 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13) x (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)
step 6 Simplify the above 52C13 equation:
=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 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13) x (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)
= 40 x 41 x 42 x 43 x 44 x 45 x 46 x 47 x 48 x 49 x 50 x 51 x 52/6227020800
= 3.9542426439112E+21/6227020800
52C13 = 635013559600
Hence,
52 choose 13 equals to 635013559600