Answer: Option third 60,480
Explanation:
Given expression [tex]\frac{9!}{3!}[/tex] is equal to [tex]\frac{9*8*7*6*5*4*3*2*1}{3*2*1}[/tex]
after cancelling out the same terms from numerator and denominator we will get
[tex]{9*8*7*6*5*4}[/tex] and after simplification we will get 72*42*20
after further simplification we will get 60,480
The evaluated form of the expression 9!/3! is given by: Option C: 60,480
Factorial of a positive integer is the result of the repeated multiplication of all the integers from 1 till that considered integer.
Thus, if we want to take factorial of 'n',(n being a positive integer), then:
[tex]n! = 1 \times 2 \times \cdots \times (n-1) \times n[/tex]
We usually write it in reverse order because in calculations, its cancellation comes useful. Thus, we have:
[tex]n! = n \times (n-1) \times \cdots \times 2 \times 1[/tex]
For this case, we've to evaluate the expression 9!/3!.
Expanding the factorials, we get:
[tex]\dfrac{9!}{3!} = \dfrac{9 \times 8 \times 7 \times 6 \times 5 \times 4\times 3\times 2\times 1}{3\times 2\times 1} = 9 \times 8 \times 7 \times 6 \times 5 \times 4\\\\\dfrac{9!}{3!} = 60480[/tex]
Thus, the evaluated form of the expression 9!/3! is given by: Option C: 60,480
Learn more about factorials here:
https://brainly.com/question/16036678
