Explanation:

Let's break it down:

- Look at the given pattern: 6 : 252.

- If you try 6 × 5 × 4 × 3 × 2 × 1, you get 720 – but that's not 252.

- Try squaring: 6³ = 216. Still doesn't fit.

- Check this: 6 × 5 × 4 × 3 + 6 = 360 + 6 = 366. Not 252.

- Or maybe, 6 × 5 × 4 + 2. Nope.

- Now, check 6 × 5 × 4 × 3/2 = 6 × 5 × 4 × 1.5 = 180. Not matching.

Here’s what actually clicks:

- 252 = 6³ + 6²

- 6³ = 216, 6² = 36; add them: 216 + 36 = 252 (Bingo!)

Apply to 5:

- 5³ = 125, 5² = 25

- 125 + 25 = 150

So, for the options given:

- Option 1: 175 (Nope)

- Option 2: 150

- Option 3: 125 (Misses the +25)

- Option 4: 225 (Too much)

Correct Answer is Option 2: 150