Obtain the number 1500 by using the operations $×, +, -, ÷$ on the numbers $1, 2, 3, 4, 5, 6, 7, 8, 9,$ in that order. Brackets are allowed, but you cannot join digits to form multi-digit numbers: for example, you may not write $1$ next to $2$ and call this $12$.
A possible solution is: $(1+2+3+4)×5×(6+7+8+9)$
Another solution: $(1÷(2×3))(4×5)(6×7+8)(9)$
My question: Is there a way to guess/know how many solutions are there?