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Nov 2011 p63 q4
2864
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.
(ii) Find the number of different ways in which Mary can choose 6 of these images if there are 2 from each folder.
(iii) Find the number of different ways in which Mary can choose 6 of these images if there are at least 3 images from the friends folder and at least 1 image from each of the other two folders.
Solution
(ii) To find the number of ways to choose 6 images with 2 from each folder, we calculate:
(iii) We need to consider different combinations of choosing images such that there are at least 3 from the friends folder and at least 1 from each of the other two folders. The possible distributions are: