#### In how many ways can 4 books be selected from a shelf of 10 distinct books, if 2 particular books must be included?Option: 1 210Option: 2 252Option: 3 168Option: 4 504

To solve this problem, we can break it down into cases based on the 2 particular books that must be included.

Case 1: The first particular book is selected.

In this case, we need to select 3 more books from the remaining 9 books (excluding the first particular book and the second particular book). We can select these 3 books in  $C(9,3)$ways.

Case 2: The second particular book is selected.

Similar to Case 1, we need to select 3 more books from the remaining 9 books (excluding the first particular book and the second particular book). Again, we can select these 3 books in  $C(9,3)$ ways.

Since we have two independent cases, we can add their results to obtain the total number of ways.

Total number of ways = Case 1 + Case 2
\begin{aligned} & =C(9,3)+C(9,3) \mid \\ & =\frac{9 !}{3 ! \times(9-3) !}+\frac{9 !}{3 ! \times(9-3) !} \\ & =84+84=168 \end{aligned}

Therefore, there are 168 ways to select 4 books from a shelf of 10 distinct books, if 2 particular books must be included.