Question

How many different arrangements of the letters in the word BETTER are there?



180

360

720

Answer 1

6*5*4*3=?/2=?

Answer 2

\[\frac{6!}{2!2!}\]
The \(6!\) counts the number of distinct arrangements. By distinct, I mean we consider repeated letters to be different from the other. For instance,
\[BE\color{red}T\color{blue}TER~~~~~~~~BE\color{blue}T\color{red}TER\]
are counted as distinct.

There are two repeated letters, T and E. The 2! (one for T and one for E) remove the arrangements that are double-counted. In other words, strings like the ones above are counted only once.

Answer 3

thank you man!