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Nov 2011 p63 q4
2793
Mary saves her digital images on her computer in three separate folders named ‘Family’, ‘Holiday’ and ‘Friends’. Her family folder contains 3 images, her holiday folder contains 4 images and her friends folder contains 8 images. All the images are different.
Find in how many ways she can arrange these 15 images in a row across her computer screen if she keeps the images from each folder together.
Solution
To solve this problem, we treat each folder as a single unit or block. Thus, we have 3 blocks: Family, Holiday, and Friends.
The number of ways to arrange these 3 blocks is given by the factorial of the number of blocks:
\(3! = 6\)
Within each block, the images can be arranged among themselves. Therefore, we calculate the factorial for each folder:
Family folder: \(3! = 6\)
Holiday folder: \(4! = 24\)
Friends folder: \(8! = 40,320\)
The total number of arrangements is the product of these factorials: