SOLUTION: There are k different books and I copies of each in a college library. The number of ways in which a student can make a selection of one or more books is

Question 1210342: There are k different books and I copies of each in a college library. The number of ways in which a student can make a selection of one or more books is
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

In choosing the books, a student can look at each book and either choose to select it or not. That's 2 choices for each book.

If there are n books in the library, that means 2 choices for each book, for a total of 2^n choices.

This problem asks for the number of ways a student can select one or more books, so selecting none of the books is not an option. So the number of ways of choosing one or more of n books is 2^n-1.

In this problem, there are k different books and I copies of each book.

Assuming the student will not be selecting more than one copy of any book, the number of books to choose from is k, and the number of ways of selecting one or more of them is 2^k-1.

If the student can select more than one copy of any book, then the number of books to choose from is (k*I), and the number of ways of choosing one or more of them is 2^(k*I)-1.

ANSWERS:
(a) not selecting multiple copies of any book: 2^k-1
(b) allowing selection of multiple copies of any book: 2^(k*I)-1

Answer by ikleyn(52779)   (Show Source): You can put this solution on YOUR website!
.
There are k different books and I copies of each in a college library.
The number of ways in which a student can make a selection of one or more books is
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

As this problem is worded in the post, it tries to confuse a reader.
In the first sentence, it introduces and considers the books and their copies as different categories.
In the question, the problem unnoticeably mixes the books and the copies into one category,
and the reader is perplexed - to which category the question does relate ?

So, to give a correct answer, we should understand this " playing words " and make it noticeable.

            Below is my solution for this different interpretation of the posed problem.

If the student can select more than one copy of any book, then the number of books (or their copies)

to choose from is (k*(I+1)), and the number of ways of choosing one or more of them is .

ANSWERS:

        (a)   not selecting multiple copies of any book:   .

        (b)   allowing selection of multiple copies of any book:   .

////////////////////////////////////

In the way how this problem is formulated and presented - - - it is not a Math problem, in its standard understanding.

It is a classic example of how thimbleriggers work in eastern bazaars and train stations, deceiving people.

If from my post you learn on how they are trying to deceive or to perplex/(to confuse) you,
then this my post is useful for you and has served its purpose.

The world is full of people who push demagogy into other people's heads.
Therefore, it is a vital skill to be able to recognize deception, omissions and demagogy.

In real Math problems written by professional math writers, you will never encounter such formulations.
They are forbidden and never used.
So, if you see an ambiguous formulation, it means that you have one of two cases.
Either this writer is unprofessional as a creator of math problems, or he is deliberately preparing a trap for you.

This "either-or" in the last my sentence is INCLUSIVE, which means
that both cases in one package simultaneously are not excluded.

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