7C5: 7 choose 5 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 5 elements at a time from 8 distinct elements without considering the order of elements.
nCk of 7C5:
7 CHOOSE 5 = 21
where,
7 is the total number of distinct elements (n),
5 is the the number of elements drawn or choosen at a time (k),
21 is the total number of possible combination (C).
7C5 Points to Remember:
7C5 is the type of nCr or nCk problem. The below 7 choose 5 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 5 elements at a time from 7 distinct elements without considering the order of elements.
Solved Example: :
what is 7 choose 5?
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) = 5
What to be found:
Find the total number of possible combinations while choosing 5 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 5:
5! = 1 x 2 x 3 x 4 x 5
step 4 Find the factorial of difference between 7 and 5:
(7 - 5)! = 2!
2! = 1 x 2
step 5 Apply the values of 7!, 5! and 2! in the nCk formula:
nCk = n!/k! (n - k)!
7C5 =7!/5! x 2!
=1 x 2 x 3 x 4 x 5 x 6 x 7/(1 x 2 x 3 x 4 x 5) x (1 x 2)
step 6 Simplify the above 7C5 equation:
=1 x 2 x 3 x 4 x 5 x 6 x 7/(1 x 2 x 3 x 4 x 5) x (1 x 2)
= 6 x 7/2
= 42/2
7C5 = 21
Hence,
7 choose 5 equals to 21