The problem provided involves evaluating the following expression:

$\left( \frac{5}{6} + 0.1667 \right) \div \left( \frac{7}{6} - 1.833 \right) \times \left( \frac{3}{5} - 3 \right)$

Let me solve this step by step.

Step 1: Simplify each part inside the parentheses

1. $\frac{5}{6} + 0.1667$
2. $\frac{7}{6} - 1.833$
3. $\frac{3}{5} - 3$

Step 2: Evaluate the operations

1. $\frac{5}{6} + 0.1667 = 0.8333 + 0.1667 = 1$
2. $\frac{7}{6} - 1.833 = 1.1667 - 1.833 = -0.6663$
3. $\frac{3}{5} - 3 = 0.6 - 3 = -2.4$

Step 3: Combine the results

Now we compute:

$\left( 1 \right) \div \left( -0.6663 \right) \times \left( -2.4 \right)$

First, divide $1$ by $-0.6663$:

$1 \div -0.6663 \approx -1.5$

Then, multiply by $-2.4$:

$-1.5 \times -2.4 = 3.6$

Final Answer:

The answer is $3.6$, which corresponds to option E.

Would you like more details on any step? Here are some related questions you could explore:

1. What is the importance of parentheses in mathematical expressions?
2. How do you handle operations with negative numbers?
3. What are some tips for simplifying fractions and decimals?
4. How do you multiply and divide fractions efficiently?
5. Can approximations like $0.1667$ affect the final result?

Tip: When working with decimals and fractions, it is useful to round decimals carefully to avoid errors in larger calculations.