Question

(a)
Evaluate each of the following:
(i)
10! X 20!
17! X 9!


​

Answer 1

`10!\:* \:20!=\:8.82851\:*\:10^(24)`

`17!\:* \:9!\:=\:1.29072\:* \:10^(20)`

Explanation:

1)

Given the expression

`10!* \:20!`

`\mathrm{Apply\:factorial\:rule}:\quad \:n!=1* 2* 3* \ldots * \:n`

`10!=1* \:2* \:3* \:4* \:5* \:6* \:7* \:8* \:9* \:10`

`20!=1* \:2* \:3* \:4* \:5* \:6* \:7* \:8* \:9* \:10* \:11* \:12* \:13* \:14* \:15* \:16* \:17* \:18* \:19* \:20`

Now, multiplying the result

`10!* \:20!= 1* \:2* \:3* \:4* \:5* \:6* \:7* \:8* \:9* \:10* \:1* \:2* \:3* \:4* \:5* \:6* \:7* \:8* \:9* \:10* \:11* \:12* \:13* \:14* \:15* \:16* \:17* \:18* \:19* \:20`

so

`10!\:* \:20!=\:8.82851\:*\:10^(24)`

Thus, we conclude that:

`10!\:* \:20!=\:8.82851\:*\:10^(24)`

2)

Given the expression

`17!\:* \:9!`

`\mathrm{Apply\:factorial\:rule}:\quad \:n!=1* 2* 3* \ldots * \:n`

`17!=1* \:2* \:3* \:4* \:5* \:6* \:7* \:8* \:9* \:10* \:11* \:12* \:13* \:14* \:15* \:16* \:17`

`9!=1* \:2* \:3* \:4* \:5* \:6* \:7* \:8* \:9`

Now, multiplying the result

`17!\:* \:9!=1* \:2* \:3* \:4* \:5* \:6* \:7* \:8* \:9* \:10* \:11* \:12* \:13* \:14* \:15* \:16* \:17* \:1* \:2* \:3* \:4* \:5* \:6* \:7* \:8* \:9`

so

`17!\:* \:9!\:=\:1.29072\:* \:10^(20)`

Thus, we conclude that:

`17!\:* \:9!\:=\:1.29072\:* \:10^(20)`