10C3: 10 choose 3 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 3 elements at a time from 8 distinct elements without considering the order of elements.
nCk of 10C3:
10 CHOOSE 3 = 120
where,
10 is the total number of distinct elements (n),
3 is the the number of elements drawn or choosen at a time (k),
120 is the total number of possible combination (C).
10C3 Points to Remember:
10C3 is the type of nCr or nCk problem. The below 10 choose 3 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 3 elements at a time from 10 distinct elements without considering the order of elements.
Solved Example: :
what is 10 choose 3?
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) = 3
What to be found:
Find the total number of possible combinations while choosing 3 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 3:
3! = 1 x 2 x 3
step 4 Find the factorial of difference between 10 and 3:
(10 - 3)! = 7!
7! = 1 x 2 x 3 x 4 x 5 x 6 x 7
step 5 Apply the values of 10!, 3! and 7! in the nCk formula:
nCk = n!/k! (n - k)!
10C3 =10!/3! x 7!
=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10/(1 x 2 x 3) x (1 x 2 x 3 x 4 x 5 x 6 x 7)
step 6 Simplify the above 10C3 equation:
=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10/(1 x 2 x 3) x (1 x 2 x 3 x 4 x 5 x 6 x 7)
= 8 x 9 x 10/6
= 720/6
10C3 = 120
Hence,
10 choose 3 equals to 120