Four coffee mugs and a water bottle are to be chosen from eight different coffee mugs and four different water bottles and arranged in a row on the shelf with the water bottle in the center. What is the total number of such arrangements?
101600
202500
201600
210600
Given that,
There are 8 coffee mugs and 4 water bottles.
From 8 coffee mugs, the number of ways to choose 4 coffee mugs is given by,
From 4 water bottles, the number of ways to choose 1 water bottle is given by,
From the given, the water bottle should be placed in the center.
As a result, the remaining 6 coffee mugs can be organized in 6! different ways.
Thus, the required number of arrangements is given by,
Therefore, the total number of arrangements is 201600 ways.
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