Correct Answer - Option 4 : 5040
Concept:
Number of permutations in a word:
If a word contains n number of letters and every letter a1, a2, ... repeats for r1, r2, .. 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.