Question

Evaluate each expression.

6! =



3! • 2! =



StartFraction 6 factorial Over 3 factorial EndFraction =

Answer 1

720

12

120

Explanation:

Answer 2

720

12

120

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 (6!)/(3!)=(6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1)/(3\cdot 2\cdot 1)`

`\displaystyle (6!)/(3!)= (720)/(6)=120`