7C3: 7 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 7C3:
7 CHOOSE 3 = 35
where,
7 is the total number of distinct elements (n),
3 is the the number of elements drawn or choosen at a time (k),
35 is the total number of possible combination (C).
7C3 Points to Remember:
7C3 is the type of nCr or nCk problem. The below 7 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 7 distinct elements without considering the order of elements.
Solved Example: :
what is 7 choose 3?
step 1 Address the input parameters and observe what to be found:
Input values:
Total number of distinct elements (n) = 7
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 7 distinct elements without considering the order of elements.
step 2 Find the factorial of 7:
7! = 1 x 2 x 3 x 4 x 5 x 6 x 7
step 3 Find the factorial of 3:
3! = 1 x 2 x 3
step 4 Find the factorial of difference between 7 and 3:
(7 - 3)! = 4!
4! = 1 x 2 x 3 x 4
step 5 Apply the values of 7!, 3! and 4! in the nCk formula:
nCk = n!/k! (n - k)!
7C3 =7!/3! x 4!
=1 x 2 x 3 x 4 x 5 x 6 x 7/(1 x 2 x 3) x (1 x 2 x 3 x 4)
step 6 Simplify the above 7C3 equation:
=1 x 2 x 3 x 4 x 5 x 6 x 7/(1 x 2 x 3) x (1 x 2 x 3 x 4)
= 5 x 6 x 7/6
= 210/6
7C3 = 35
Hence,
7 choose 3 equals to 35