17C3: 17 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 17C3:
17 CHOOSE 3 = 680
where,
17 is the total number of distinct elements (n),
3 is the the number of elements drawn or choosen at a time (k),
680 is the total number of possible combination (C).
17C3 Points to Remember:
17C3 is the type of nCr or nCk problem. The below 17 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 17 distinct elements without considering the order of elements.
Solved Example: :
what is 17 choose 3?
step 1 Address the input parameters and observe what to be found:
Input values:
Total number of distinct elements (n) = 17
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 17 distinct elements without considering the order of elements.
step 2 Find the factorial of 17:
17! = 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
step 3 Find the factorial of 3:
3! = 1 x 2 x 3
step 4 Find the factorial of difference between 17 and 3:
(17 - 3)! = 14!
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
step 5 Apply the values of 17!, 3! and 14! in the nCk formula:
nCk = n!/k! (n - k)!
17C3 =17!/3! x 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) 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)
step 6 Simplify the above 17C3 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/(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)
= 15 x 16 x 17/6
= 4080/6
17C3 = 680
Hence,
17 choose 3 equals to 680