10C2: 10 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 10C2:
10 CHOOSE 2 = 45
where,
10 is the total number of distinct elements (n),
2 is the the number of elements drawn or choosen at a time (k),
45 is the total number of possible combination (C).
10C2 Points to Remember:
10C2 is the type of nCr or nCk problem. The below 10 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 10 distinct elements without considering the order of elements.
Solved Example: :
what is 10 choose 2?
step 1 Address the input parameters and observe what to be found:
Input values:
Total number of distinct elements (n) = 10
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 10 distinct elements without considering the order of elements.
step 2 Find the factorial of 10:
10! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10
step 3 Find the factorial of 2:
2! = 1 x 2
step 4 Find the factorial of difference between 10 and 2:
(10 - 2)! = 8!
8! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8
step 5 Apply the values of 10!, 2! and 8! in the nCk formula:
nCk = n!/k! (n - k)!
10C2 =10!/2! x 8!
=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10/(1 x 2) x (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8)
step 6 Simplify the above 10C2 equation:
=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10/(1 x 2) x (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8)
= 9 x 10/2
= 90/2
10C2 = 45
Hence,
10 choose 2 equals to 45