Answer :
Given:
[tex]4 + 9 + 16 \div 4 - 8 -3 \times 5[/tex]
To find:
The number of possible solutions, if the Order of Operations did not exist.
Solution:
We have,
[tex]4 + 9 + 16 \div 4 - 8 -3 \times 5[/tex]
Now,
Case 1:
[tex][4 + 9 + 16] \div [4 - 8 -(3 \times 5)]=29\div (4 - 8 -15)[/tex]
[tex]4 + 9 + 16 \div 4 - 8 -(3 \times 5)=-\dfrac{29}{19}[/tex]
Case 2:
[tex][4 + 9 + 16] \div (4 - 8 -3) \times 5=29\div (-7\times 5)[/tex]
[tex]4 + 9 + 16 \div (4 - 8 -3) \times 5=-\dfrac{29}{35}[/tex]
Case 3:
[tex]4 + 9 + (16 \div 4) - 8 -(3 \times 5)=4+9+4-8-15[/tex]
[tex]4 + 9 + (16 \div 4) - 8 -(3 \times 5)=-6[/tex]
Many more possibilities are there.
Therefore, there are more than 3 possible solutions.