There are 7 different books in a library. A girl can borrow book B if only book A is borrowed. In how many ways can she borrow 3 books ?

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There are 7 different books in a library. A girl can borrow book B if only book A is borrowed. In how many ways can she borrow 3 books ?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\(\large \color{black}{\begin{align} & \normalsize \text{There are 7 different books in a library. }\hspace{.33em}\\~\\ & \normalsize \text{A girl can borrow book B if only book A is borrowed.} \hspace{.33em}\\~\\ & \normalsize \text{In how many ways can she borrow 3 books ?} \hspace{.33em}\\~\\ & a.)\ 15 \hspace{.33em}\\~\\ & b.)\ 20 \hspace{.33em}\\~\\ & c.)\ 25 \hspace{.33em}\\~\\ & d.)\ 30 \hspace{.33em}\\~\\ \end{align}}\)
is there any specific arrange for A and B ?
``` A girl can borrow book B if only book A is borrowed ``` Must book A be borrowed by the girl or by someone else?

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Other answers:

  • phi
25
book B can be borrowed only if book A is borrowed
yes 25 is answer given , how u got it
I am confused by the question. But phi is not :)
"A girl can borrow book B if only book A is borrowed" i think "Must book A be borrowed by the girl "
lol m also confused by thhe question
"A girl can borrow book B if only she also borrows book A" is the intended wording if 25 is the final answer.
  • phi
First, order does not matter. I broke the problem into two parts. say one of the 3 books we choose is A. then we have a choice of 6C2 for the other two. that is 15 combinations say we did not choose A. then that means we can not choose B either. that leaves 5 books from which to choose 3 5C3= 10 more combinations 15+10= 25
"A girl can borrow book B if only she also borrows book A" is the intended wording if 25 is the final answer. yea i think so ,
thnx

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