10C10: 10 choose 10 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 10 elements at a time from 8 distinct elements without considering the order of elements.
nCk of 10C10:
10 CHOOSE 10 = 1
where,
10 is the total number of distinct elements (n),
10 is the the number of elements drawn or choosen at a time (k),
1 is the total number of possible combination (C).
10C10 Points to Remember:
10C10 is the type of nCr or nCk problem. The below 10 choose 10 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 10 elements at a time from 10 distinct elements without considering the order of elements.
Solved Example: :
what is 10 choose 10?
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) = 10
What to be found:
Find the total number of possible combinations while choosing 10 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 10:
10! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10
step 4 Find the factorial of difference between 10 and 10:
(10 - 10)! = 0!
0! = 1
step 5 Apply the values of 10!, 10! and 0! in the nCk formula:
nCk = n!/k! (n - k)!
10C10 =10!/10! x 0!
=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 10) x (1)
step 6 Simplify the above 10C10 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 10) x (1)
= 1/1
= 1/1
10C10 = 1
Hence,
10 choose 10 equals to 1