7C2: 7 CHOOSE 2

7C2: 7 choose 2 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 2 elements at a time from 8 distinct elements without considering the order of elements.

nCk of 7C2:
7 CHOOSE 2 = 21
where,
7 is the total number of distinct elements (n),
2 is the the number of elements drawn or choosen at a time (k),
21 is the total number of possible combination (C).

7C2 Points to Remember:

• 7 CHOOSE 2 can also be denoted as 7C2.
• Draw 2 out of 7 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
• In 21 possible combinations, AB and BA are not considered as different events.
• AB and BA considered as a single combination in 21 events.

7C2 is the type of nCr or nCk problem. The below 7 choose 2 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 2 elements at a time from 7 distinct elements without considering the order of elements.

Solved Example: :
what is 7 choose 2?

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) = 2

What to be found:
Find the total number of possible combinations while choosing 2 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 2:
2! = 1 x 2

step 4 Find the factorial of difference between 7 and 2:
(7 - 2)! = 5!
5! = 1 x 2 x 3 x 4 x 5

step 5 Apply the values of 7!, 2! and 5! in the nCk formula:
nCk = n!/k! (n - k)!
7C2 =7!/2! x 5!

=1 x 2 x 3 x 4 x 5 x 6 x 7/(1 x 2) x (1 x 2 x 3 x 4 x 5)

step 6 Simplify the above 7C2 equation:
=1 x 2 x 3 x 4 x 5 x 6 x 7/(1 x 2) x (1 x 2 x 3 x 4 x 5)

= 6 x 7/2
= 42/2

7C2 = 21

Hence,
7 choose 2 equals to 21