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One artist donates 3 different sculptures and 6 different vases to the museum.
The exhibits will be arranged in a row. Find the number of possible arrangements
if each sculpture must be placed between two vases.
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The sculptures are placed in the gaps between the vases.
In all, there are 6 different vases and 6-1 = 5 gaps between them.
Of these 5 gaps, we can select 3 gaps to place sculptures by 
= 
= 5*2 = 10 different ways.
So, we have 10 different options to choose 3 gaps for sculptures;
3! = 6 ways to order these 3 sculptures (permutations of 3 objects),
and 6! = 720 ways to order 6 vases (permutations of 6 objects).
Thus, in all, there are 10*6*720 = 43200 different arrangements. ANSWER
Solved.
