Victor__ wrote:

I think this is a poor-quality question and I don't agree with the explanation. The answer seems to be wrongly calculated.

Hi

Victor__it would be great if you could explain what exactly is wrong with the official solution?

As per the question there are two possibilities -

A. take \(1\) large book \(AND\) \(4\) small books. Mathematically this can be represented as -

\(1\) large book can be selected from \(2\) large books in \(2_C_1\) and remaining \(4\) small books can be selected from \(8\) small books in \(8_C_4\)

therefore total number of ways = \(2_C_1\) \(*\) \(8_C_4 = 140\)

\(OR\)

B. take \(5\) small books and no large books. Mathematically it can be represented as -

\(5\) small books can be selected from \(8\) books in \(8_C_5 = 56\)

Therefore total number of ways = \(140+56 = 196\)