Thinking Mathematically (6th Edition)

$210$ ways
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 ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$. ---------------- Arrangements: order is important. There are n=7 distinct letters (no duplicates) from which r=4 are taken. The formula ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$ applies. ${}_{7}P_{4}=\displaystyle \frac{7!}{3!}=7\times 6\times 5=$ $= 210$ ways