## Thinking Mathematically (6th Edition)

The statement is false. An example of a true statement: Even though BET and BEE are both three letter words, the number of permutations for each of them differ. BET has 3!=6 permutations. BEE has $\displaystyle \frac{3!}{2!}$=3 permutations.
-------------------- For the word BET, all three letters are different, so it is true that the number of permutations is $3!=6.$ For the word BEE, there is a group of duplicates (two Es), for which the formula is different, $\displaystyle \frac{3!}{2!}=\frac{6}{2}=3$ The statement is false. An example of a true statement: Even though BET and BEE are three letter words, the number of permutations for each of them differ. BET has 3!=6 permutations. BEE has $\displaystyle \frac{3!}{2!}$=3 permutations.