10C9: 10 choose 9 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 9 elements at a time from 8 distinct elements without considering the order of elements.
nCk of 10C9:
10 CHOOSE 9 = 10
where,
10 is the total number of distinct elements (n),
9 is the the number of elements drawn or choosen at a time (k),
10 is the total number of possible combination (C).
10C9 Points to Remember:
10C9 is the type of nCr or nCk problem. The below 10 choose 9 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 9 elements at a time from 10 distinct elements without considering the order of elements.
Solved Example: :
what is 10 choose 9?
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) = 9
What to be found:
Find the total number of possible combinations while choosing 9 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 9:
9! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9
step 4 Find the factorial of difference between 10 and 9:
(10 - 9)! = 1!
1! = 1
step 5 Apply the values of 10!, 9! and 1! in the nCk formula:
nCk = n!/k! (n - k)!
10C9 =10!/9! x 1!
=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 4 x 5 x 6 x 7 x 8 x 9) x (1)
step 6 Simplify the above 10C9 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 4 x 5 x 6 x 7 x 8 x 9) x (1)
= 10/1
= 10/1
10C9 = 10
Hence,
10 choose 9 equals to 10