Discussion

Explanation:

There is a total of 5 + 4 + 3 = 12 different books on the shelf.

We have to pick at least book. Let us name these books as

Maths: M₁, M₂, M₃, M₄ and M₅.
Reasoning: R₁, R₂, R₃ and R₄.
English: E₁, E₂ and E₃.

There are two possibilities for each of these books i.e., either the book will be picked or not picked.

∴ Total possibilities for picking books = 2¹².

Now out of these 2¹² possibilities, there would be one possibility when no book is picked.

∴ Number of ways of picking at least 1 book = 2¹² - 1 = 4096 – 1 = 4095 ways.

Hence, 4095.

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