52C4: 52 CHOOSE 4
52C4: 52 choose 4 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 4 elements at a time from 8 distinct elements without considering the order of elements.
nCk of 52C4:
52 CHOOSE 4 = 270725
where,
52 is the total number of distinct elements (n),
4 is the the number of elements drawn or choosen at a time (k),
270725 is the total number of possible combination (C).
52C4 Points to Remember:
- 52 CHOOSE 4 can also be denoted as 52C4.
- Draw 4 out of 52 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
- In 270725 possible combinations, AB and BA are not considered as different events.
- AB and BA considered as a single combination in 270725 events.
How-to find nCk: 52 CHOOSE 4?
52C4 is the type of nCr or nCk problem. The below 52 choose 4 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 4 elements at a time from 52 distinct elements without considering the order of elements.
Solved Example: :
what is 52 choose 4?
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) = 4
What to be found:
Find the total number of possible combinations while choosing 4 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 4:
4! = 1 x 2 x 3 x 4
step 4 Find the factorial of difference between 52 and 4:
(52 - 4)! = 48!
48! = 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
step 5 Apply the values of 52!, 4! and 48! in the nCk formula:
nCk = n!/k! (n - k)!
52C4 =52!/4! x 48!
=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 (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)
step 6 Simplify the above 52C4 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 (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)
= 49 x 50 x 51 x 52/24
= 6497400/24
52C4 = 270725
Hence,
52 choose 4 equals to 270725