13C2: 13 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 13C2:
13 CHOOSE 2 = 78
where,
13 is the total number of distinct elements (n),
2 is the the number of elements drawn or choosen at a time (k),
78 is the total number of possible combination (C).
13C2 Points to Remember:
13C2 is the type of nCr or nCk problem. The below 13 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 13 distinct elements without considering the order of elements.
Solved Example: :
what is 13 choose 2?
step 1 Address the input parameters and observe what to be found:
Input values:
Total number of distinct elements (n) = 13
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 13 distinct elements without considering the order of elements.
step 2 Find the factorial of 13:
13! = 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
step 3 Find the factorial of 2:
2! = 1 x 2
step 4 Find the factorial of difference between 13 and 2:
(13 - 2)! = 11!
11! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11
step 5 Apply the values of 13!, 2! and 11! in the nCk formula:
nCk = n!/k! (n - k)!
13C2 =13!/2! x 11!
=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/(1 x 2) x (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11)
step 6 Simplify the above 13C2 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/(1 x 2) x (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11)
= 12 x 13/2
= 156/2
13C2 = 78
Hence,
13 choose 2 equals to 78