Correct Answer - Option 4 : 5040

**Concept:**

**Number of permutations in a word:**

If a word contains n number of letters and every letter a_{1}, a_{2}, ... repeats for r_{1}, r_{2}, .. times then the number of permutations in the word is given by: \(\rm \dfrac{n!}{r_1!r_2!\cdots}\)

**Calculation:**

Observe that the number of letters in the word BASEBALL is 8.

Therefore, n = 8.

Now we will count the repeated letters:

B - 2

A - 2

S - 1

E - 1

L - 2

Thus, the possible number of permutations is calculated as follows:

\(\begin{align*} \dfrac{8!}{2!2!1!1!2!} &= \dfrac{8!}{2!2!2!}\\ &= \dfrac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{2\times 1\times 2\times 1\times 2\times 1}\\ &= 7\times 6\times 5\times 4\times 3\times 2\\ &= 5040 \end{align*}\)

Therefore, the possible number of permutations is 5040.