How many different arrangements of all the letters of the word BANANA are possible?

Explanation

1. 01

   BANANA has 6 letters: A three times, N twice, B once.

2. 02

   Swapping identical letters gives nothing new, so divide by the repeats.

3. 03

   Arrangements $= \frac{6!}{3! \times 2!} = \frac{720}{12} = 60$.