Question

There are 3 different mathematics books and 4 different physics books in a shelf. Then the number of ways these books can be arranged so that the mathematics books are together is:

• A. 144
• B. 120
• C. 520
• D. 720
• E. 620

Hint:

When arranging books with a condition (like keeping a group together), treat the group as a single block and then arrange the rest of the items.

Answer 1

The Correct Option is D

To solve this problem, we treat the 3 mathematics books as a single block, since they must be together.
So, now we have:
- 1 block of mathematics books, and
- 4 physics books.
This gives us a total of \( 1 + 4 = 5 \) items (the block and the 4 physics books) to arrange.
The number of ways to arrange these 5 items is \( 5! \).
Now, within the block of mathematics books, the 3 mathematics books can be arranged in \( 3! \) ways.
Thus, the total number of ways to arrange the books is: \[ 5! \times 3! = 120 \times 6 = 720 \] Thus, the correct answer is option (D), 720.