# In how many ways can 3 monitors be oriented and placed on a desk?

There are $3$ distinguishable monitors and each monitor can be oriented in $4$ unique ways. In how many ways can you arrange them on a desk? ($3$ positions in total)

My attempt:

There are $3!$ ways to arrange the monitors without worrying about their orientation. For each arrangement there are $4^3$ ways to orient the monitors since each monitor can be oriented in 4 unique ways. Therefore there are $3! \times 4^3 = 384$ ways to arrange the monitors

• That is correct. Commented Apr 8, 2015 at 16:04
• Agreed. Your answer is correct! Commented Apr 8, 2015 at 16:05
• Thank you, I was skeptical after many trials in my own head :) Commented Apr 8, 2015 at 16:11
• @Damien I posted a communitywiki answer (which avoids giving me and others rep for having done little to no work) so that the answer may be accepted to remove this from the queue of unanswered questions. Commented Apr 8, 2015 at 16:23

By multiplication principle, the total number of ways is the product of the number of choices at each step for a combined total of $3!4^3 = 384$ number of ways to arrange the monitors on the desk.