Question:
There are P copies of n-different books. The number of different ways in which a non-empty selection can be made from them is ________.
There are P copies of n-different books. The number of different ways in which a non-empty selection can be made from them is ________.
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There are P copies of n-different books. The number of different ways in which a non-empty selection can be made from them is ____.
Updated On: Apr 15, 2026
- $(P+1)^{n}-1$
- $P^{n}-1$
- $(P+1)^{n-1}-1$
- None of these
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The Correct Option is A
Solution and Explanation
Step 1: Selection for one book
For any book, we can choose 0, 1, 2, ..., P copies. Total $P+1$ ways.
Step 2: Total Selections
Since there are $n$ different books, total ways $= (P+1) \times (P+1) \times \dots$ ($n$ times) $= (P+1)^n$.
Step 3: Non-empty Condition
Exclude the case where zero copies of all books are selected.
Step 4: Conclusion
Result $= (P+1)^n - 1$.
Final Answer: (A)
For any book, we can choose 0, 1, 2, ..., P copies. Total $P+1$ ways.
Step 2: Total Selections
Since there are $n$ different books, total ways $= (P+1) \times (P+1) \times \dots$ ($n$ times) $= (P+1)^n$.
Step 3: Non-empty Condition
Exclude the case where zero copies of all books are selected.
Step 4: Conclusion
Result $= (P+1)^n - 1$.
Final Answer: (A)
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