The word OPTICAL consists of 7 distinct letters:
O, P, T, I, C, A, L
It contains 3 vowels: O, I, A and 4 consonants: P, T, C, L.

Step 1: Treating the vowels as a single unit

Since the vowels O, I, A must always be together, we can treat them as one unit. This reduces the problem to arranging the following 5 units:

• (OIA) as a single unit
• P, T, C, L (the four consonants)

The number of ways to arrange these 5 units is:

5!=5×4×3×2×1=1205! = 5 × 4 × 3 × 2 × 1 = 1205!=5×4×3×2×1=120
Step 2: Arranging the vowels within their unit

The vowels O, I, A can be arranged among themselves in:

3!=3×2×1=63! = 3 × 2 × 1 = 63!=3×2×1=6
Step 3: Calculating the total number of arrangements

Since these two arrangements are independent, the total number of ways to arrange the letters of OPTICAL while keeping the vowels together is:

5!×3!=120×6=7205! \times 3! = 120 \times 6 = 7205!×3!=120×6=720
Final Answer:

720 different ways.