2C2: 2 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 2C2:
2 CHOOSE 2 = 1
where,
2 is the total number of distinct elements (n),
2 is the the number of elements drawn or choosen at a time (k),
1 is the total number of possible combination (C).
2C2 Points to Remember:
2C2 is the type of nCr or nCk problem. The below 2 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 2 distinct elements without considering the order of elements.
Solved Example: :
what is 2 choose 2?
step 1 Address the input parameters and observe what to be found:
Input values:
Total number of distinct elements (n) = 2
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 2 distinct elements without considering the order of elements.
step 2 Find the factorial of 2:
2! = 1 x 2
step 3 Find the factorial of 2:
2! = 1 x 2
step 4 Find the factorial of difference between 2 and 2:
(2 - 2)! = 0!
0! = 1
step 5 Apply the values of 2!, 2! and 0! in the nCk formula:
nCk = n!/k! (n - k)!
2C2 =2!/2! x 0!
=1 x 2/(1 x 2) x (1)
step 6 Simplify the above 2C2 equation:
=1 x 2/(1 x 2) x (1)
= 1/1
= 1/1
2C2 = 1
Hence,
2 choose 2 equals to 1