Answer: There are 35 ways to arrange on a shelf.
Explanation:
Since we have given that
Number of identical footballs = 4
Number of identical basketballs = 3
We need to find the number of ways that the above can be ordered on a shelf.
Total number of books = 4+3 = 7
So, it becomes,
![=(7!)/(4!* 3!)\\\\=(5040)/(144)\\\\=35](https://img.qammunity.org/2020/formulas/mathematics/high-school/qen4rjqbu2hfkh8bdvi5g5q5cmvrc82or1.png)
Since there are 4 identical footballs i.e. 4! and 3 identical basketballs i.e. 3!. so, we divide the identical part with the whole part.
Hence, there are 35 ways to arrange on a shelf.