Question

Evaluate each expression.

Answer 1

Answer:

720

12

120

Step-by-step explanation:

 

Answer 2

Answer:

720

12

120

Step-by-step explanation:

Factorials

We must recall that the factorial of a number n (positive or zero) is the product of all the integers from n down to 1

$n!= n(n-1)(n-2)...1$

Let's evaluate the given expressions

$6!=6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1=720$

Similarly

$3!\cdot 2!=(3\cdot 2\cdot 1)\cdot (2\cdot 1)=6\cdot 2=12$

Finally

$\displaystyle \frac{6!}{3!}=\frac{6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{3\cdot 2\cdot 1}$

$\displaystyle \frac{6!}{3!}= \frac{720}{6}=120$