#### Answer

12

#### Work Step by Step

A permutation from a group of items occurs when no item is used more than once and the order of arrangement makes a difference.
The number of permutations possible
if $r$ items are taken from $n$ items is ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$.
The number of permutations of $n$ items,
where $p$ items are identical,
$q$ items are identical,
$r$ items are identical, and so on, is $\displaystyle \frac{n!}{p!q!r!\ldots}$
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BAKE has four letters with no duplicates,
so the number of permutations is
${}_{4}P_{4}=4!=24.$
BABE has four letters, among which there are duplicates,
2 letters B, ... p=2,
and the number of distinct permutations is
$\displaystyle \frac{4!}{2!}=\frac{24}{2}=12$