25C3: 25 choose 3 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 3 elements at a time from 8 distinct elements without considering the order of elements.
nCk of 25C3:
25 CHOOSE 3 = 2300
where,
25 is the total number of distinct elements (n),
3 is the the number of elements drawn or choosen at a time (k),
2300 is the total number of possible combination (C).
25C3 Points to Remember:
25C3 is the type of nCr or nCk problem. The below 25 choose 3 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 3 elements at a time from 25 distinct elements without considering the order of elements.
Solved Example: :
what is 25 choose 3?
step 1 Address the input parameters and observe what to be found:
Input values:
Total number of distinct elements (n) = 25
The number of elements drawn at a time (k) = 3
What to be found:
Find the total number of possible combinations while choosing 3 elements at a time from 25 distinct elements without considering the order of elements.
step 2 Find the factorial of 25:
25! = 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
step 3 Find the factorial of 3:
3! = 1 x 2 x 3
step 4 Find the factorial of difference between 25 and 3:
(25 - 3)! = 22!
22! = 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
step 5 Apply the values of 25!, 3! and 22! in the nCk formula:
nCk = n!/k! (n - k)!
25C3 =25!/3! x 22!
=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/(1 x 2 x 3) 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)
step 6 Simplify the above 25C3 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/(1 x 2 x 3) 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)
= 23 x 24 x 25/6
= 13800/6
25C3 = 2300
Hence,
25 choose 3 equals to 2300