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Question

From 12 books in how many ways can a selection of 5 be made, (1) when one specified book is always included; (2) when on specified book is always excluded?

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Solution

(i) Since the specified book is to be included in every selection, we have only to choose 4 out of the remaining 11
Hence the number of ways = 11C4
=11×10×9×81×2×3×4=330
(2) Since the specified book is always to be excluded, we have to select the 5 books out of the remaining 11.
Hence the number of ways = 11C5
=11×10×9×8×71×2×3×4×5=462

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