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:
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:
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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.
Updated On: Apr 7, 2026
- 144
- 120
- 520
- 720
- 620
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The Correct Option is D
Solution and Explanation
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.
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.
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