Final answer:
To evaluate 10!/4! x (10-4)!, we first simplify 10! as 10·9·8·7·6·5·4! and cancel out the common 4! factor in the numerator and denominator. Then we recognize that (10-4)! is 6!, which cancels out with part of the numerator, leaving us with a final result of 15120 after dividing by 2.
Step-by-step explanation:
Evaluating the Expression 10!/4! x (10-4)!
To evaluate the expression 10!/4! x (10-4)!, we first need to understand what factorial means. A factorial of a number, indicated by an exclamation mark (!), is the product of all positive integers less than or equal to that number. For example, 4! (four-factorial) is 4·3·2·1, which equals 24. We can apply this knowledge to the expression in question.
Here's how we can simplify the expression step-by-step:
- 10! means 10·9·8·7·6·5·4!.
- Since 4! appears in both the numerator and the denominator, it cancels out, leaving us with 10·9·8·7·6·5.
- (10-4)! is equivalent to 6!, which simplifies to 6·5·4·3·2·1.
- Therefore, our expression simplifies to 10·9·8·7 divided by 2·1, as 6, 5, 4, and 3 cancel out as well.
- The final result is 10·9·8·7 divided by 2, which equals 15120.
The simplified result of the expression is 15120.