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| 1. |
There are n different books and m copies of each in a college library. The number of ways in which a selection of one or more books is : |
| Answer» <p style="text-align:justify"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000"><strong>Correct option (d) (m + 1)<sup>n</sup> − 1</strong></span></span></p><p style="text-align:justify"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000"><strong>Explanation:</strong></span></span></p><p style="text-align:justify"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">In the case of each book we may take 0, 1, 2, 3, ... m copies. </span></span></p><p style="text-align:justify"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">∴ We may deal with each book in (m + 1) ways and therefore with all the books in (m + 1) n ways. But this includes the case where all books are rejected and no selection is made. So, the number of ways in which selection can be made </span></span></p><p style="text-align:justify"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">= (m + 1)<sup>n</sup> − 1</span></span></p> | |