Question

Evaluate the expression. StartFraction 9 factorial Over 3 factorial EndFraction 3 6 60,480 362,874

Answer 1

60480

Explanation:

Answer 2

60,480 is the correct answer.

Explanation:

First of all, let us have a look at the formula of factorial of a number 'n':

`n! = n * (n-1) * (n-2) * ...... * 1`

i.e. multiply n with (n-1) then by (n-2) upto 1.

Keep on subtracting 1 from the number and keep on multiplying until we reach to 1.

So,
`9!` can be written as:
`9 * 8 * 7 * ...... * 1`

Similarly
`3!` can be written as:
`3 * 2 * 1`

Re-writing
`9 !` :

`9 * 8 * 7 * ...... 3 * 2 * 1\\\Rightarrow 9 * 8 * 7 * ...... 3 !`

Now, the expression to be evaluated:

`(9!)/(3!) = (9 * 8 * 7 * ..... * 3!)/(3!)\\\Rightarrow 9 * 8 * 7 * 6 * 5 * 4\\\Rightarrow 60480`