# 10C5: 10 CHOOSE 5 10C5: 10 choose 5 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 5 elements at a time from 8 distinct elements without considering the order of elements.

nCk of 10C5:
10 CHOOSE 5 = 252
where,
10 is the total number of distinct elements (n),
5 is the the number of elements drawn or choosen at a time (k),
252 is the total number of possible combination (C).

10C5 Points to Remember:

• 10 CHOOSE 5 can also be denoted as 10C5.
• Draw 5 out of 10 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
• In 252 possible combinations, AB and BA are not considered as different events.
• AB and BA considered as a single combination in 252 events.

For values other than 10 choose 5, use this below tool:
CHOOSE

## How-to find nCk: 10 CHOOSE 5?

10C5 is the type of nCr or nCk problem. The below 10 choose 5 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 5 elements at a time from 10 distinct elements without considering the order of elements.

Solved Example: :
what is 10 choose 5?

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) = 5

What to be found:
Find the total number of possible combinations while choosing 5 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 5:
5! = 1 x 2 x 3 x 4 x 5

step 4 Find the factorial of difference between 10 and 5:
(10 - 5)! = 5!
5! = 1 x 2 x 3 x 4 x 5

step 5 Apply the values of 10!, 5! and 5! in the nCk formula:
nCk = n!/k! (n - k)!
10C5 =10!/5! x 5!

=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 (1 x 2 x 3 x 4 x 5)

step 6 Simplify the above 10C5 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 (1 x 2 x 3 x 4 x 5)

= 6 x 7 x 8 x 9 x 10/120
= 30240/120

10C5 = 252

Hence,
10 choose 5 equals to 252 