Well, you could assign a letter to each piece of luggage like so...
A, B, C, D, E, F, G
What you could then do is set it against a table (a configuration table to be precise) with the same letters, and repeat the process again. If the order of these pieces of luggage also has to be taken into account, you'll end up with more configurations.
My answer and workings are below...
35 arrangements without order taken into consideration, because there are 35 ways in which to select 3 objects from the 7 objects.
210 arrangements (35 x 6) when order is taken into consideration.
*There are 6 ways to configure 3 letters.
Alternative way to solve the problem...
Produce Pascal's triangle. If you want to know how many ways in which you can choose 3 objects from 7, select (7 3) in Pascal's triangle which is equal to 35. Now, there are 6 ways in which to configure 3 objects if you are concerned about order.
Answer:r'=0.327 m
Step-by-step explanation:
Given

angular velocity 
mass of objects 
distance of objects from stool 
Combined moment of inertia of stool and student 
Now student pull off his hands so as to increase its speed to 3.60 rev/s


Initial moment of inertia of two masses 

After Pulling off hands so that r' is the distance of masses from stool

Conserving angular momentum








Answer is 5^12 which is choice A (assuming you meant to put the ^ symbol)
The bases are the same (both are 5), so you add the exponents: 4+8 = 12. The base stays the same the entire time.
So, 5^4*5^8 = 5^(4+8) = 5^12
It is basically a square attached by a small rectangle. So figure out the area of the square and add it to the area of the rectangle and don't forget to label your answer. Hope this helped :)