Find the value of 

[18 - 3 × {3 - 3 × (3 ÷ \(\frac{1}{3}\) - 3) + 3 ÷ \(\frac{1}{3}\) + 3} - 4 × 2]

Given:

Expression: [18 - 3 × {3 - 3 × (3 ÷ (1/3) - 3) + 3 ÷ (1/3) + 3} - 4 × 2]

Concept Used:

BODMAS

Calculation:

Step 1: Simplify inside the innermost brackets:

⇒ 3 ÷ (1/3) = 3 × 3 = 9

Step 2: Substitute back into the expression:

⇒ [18 - 3 × {3 - 3 × (9 - 3) + 9 + 3} - 4 × 2]

Step 3: Simplify inside the curly brackets:

⇒ 9 - 3 = 6

⇒ 3 - 3 × 6 + 9 + 3

⇒ 3 - 18 + 9 + 3

⇒ 3 - 18 = -15

⇒ -15 + 9 = -6

⇒ -6 + 3 = -3

Step 4: Substitute back into the main expression:

⇒ [18 - 3 × (- 3) - 4 × 2]

Step 5: Simplify the remaining multiplication and subtraction:

⇒ 18 - 3 × (-3) - 4 × 2

⇒ 18 + 9 - 8

⇒ 18 + 9 = 27

⇒ 27 - 8 = 19

∴ The correct answer is 19.