Discussion
The number of arrangements of the letters of the word BANANA so that the arrangement starts and ends with the same letter, is
Answer: B
There are 16 arrangements.
BANANA has A three times, N twice and B once. B appears only once, so the word cannot start and end with B.
- Starts and ends with A: the middle four letters are B, N, N, A, arranged in \(\frac{4!}{2!} = 12\) ways.
- Starts and ends with N: the middle four letters are B, A, A, A, arranged in \(\frac{4!}{3!} = 4\) ways.
\[ 12 + 4 = 16 \]
The option 12 counts only the A case, and 20 or 24 overcount by ignoring repeated letters in the middle.
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