Explanation:

- Let's count the letters and repetitions in both words:

- 'PERMUTATIONS' (12 letters): Repeats—T(2), I(2), N(2); all others once.

- 'COMBINATIONS' (13 letters): Repeats—O(2), I(2), N(2); all others once.

- Formula for number of distinct permutations:

- If there are \( n \) letters and certain letters repeat, number of arrangements is

\( \frac{n!}{p_1!p_2!...p_k!} \), where \( p_i \) is the count of each repeated letter.

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- For 'PERMUTATIONS':

Number = \( \frac{12!}{2!2!2!} \)

- For 'COMBINATIONS':

Number = \( \frac{13!}{2!2!2!} \)

- Now, let's relate both:

$$

\frac{\text{COMBINATIONS}}{\text{PERMUTATIONS}} = \frac{13!}{12!} = 13

$$

So,

$$

y = 13x

$$

None of the options is \( y = 13x \), but let's check each:

- (1) \( x = y \) ? False, as above.

- (2) \( y = 2x \) ? False.

- (3) \( x = 4y \) ? False (\( y \) is way more than \( x \), not less).

- (4) \( y = 4x \) ? False, \( y = 13x \).

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Correct Option:

None of the provided options are correct.