Bini did not get a composite number in any of her throws.

Therefore, the outcome of the die in each throw is one out of 1, 2, 3 or 5.

If in any throw the outcome is 1, 3 or 5, the letters Bini can select are odd numbered letters of the alphabet.

Hence, in such a case, Bini can select letters out of A, C, E, G, I, K, M, O, Q, S, U, W and Y.

Therefore, there are 5 vowels and 8 consonants that Bini could use to make words.

The total number of ways she could make 3-letter words using 3 different letters from these 13 letters is

^{13}P

_{3}.

But since a word should contain atleast one vowel, all the three letters of a word cannot be consonants.

The total number of 3-letter words that can be formed from these letters such that they contain only consonants is

^{8}P

_{3}Therefore, the total number of 3-letter words that Bini could have made such that all the 3 letters are different and each word contains atleast one vowel is

= 13 × 12 × 11 – 8 × 7 × 6

= 1716 – 336

= 1380

Now, if in any throw the outcome is 2, the letters Bini can select are the even numbered letters of the alphabet i.e. B, D, F, H, J, L, N, P, R, T, V, X and Z.

Since, there are no vowels among these letters, no word containing atleast one vowel can be made.

After one throw, Bini creates all the words possible and only then throws the die for the second time.

Now, in each throw, the outcome being one among 1, 2, 3 or 5, the total number of possible outcomes are 4 × 4 = 16

We divide these possibilities in two cases

**Case (i):**

The outcome is 2 in each throw.

In this case the total number of words of the required kind that Bini can make is 0.

**Case (ii):**

In all the other 15 possibilities except the one mentioned in case (i), the number of possible words would be 1380.

This is because if the outcome is 2 in of the throws and 1, 3 or 5 in the other throw, then the total number of words that Bini can make is

0 + 1380 = 1380

Even if in both the throws, the outcome obtained is one out of 1, 3 or 5, the words made both the times would be the same and so the total number of words of the required kind will be 1380 only.

So, the answer would differ in both the cases depending on the outcome.

Since we do not know the exact outcome of the two throws, we cannot find the number of words that Bini made. Note that the question does not ask for the number of words that she could have possibly made.

Hence, option 5.