Find the distinct number of arrangements of the symbols in the string###@@\$\$\$%%%% that begin and end with % I have tried to solve this by excluding two % and performing permutation for non-distinct objects. As I excluded I left with 10 elements so n=10 and then considered non-distinct elements like # (n1=3),@(n2=2),$(n3=3),%(n4=2). n!/(n1!x n2!x n3!x n4!). Is this right approach?

So what I'm assuming: $3$ hashtags, $2$ at's, $3$ dollar signs, $4$ percentage signs
You first fix two percentages, so you are arranging $3$ hashtags, $2$ at's, $3$ dollar signs, and $2$ percentages
This can be done in $\displaystyle \frac{(3+2+3+2)!}{3!2!3!2!}=\boxed{25200}$ ways.
Basically, arrange $10$ objects, and divide because each of the TYPES of objects are indistinguishable from one another.
