April has four different basil plants and four different tomato plants. In how many ways can she arrange the plants in a row if at least two of the tomato plants must be next to each other?
+600 It's $\text{total number of ways} - \text{ways where no two tomatoes are together}$.
The first one is $8!$.
The second one is harder. We can have $TBTBTBTB$ or $BTBTBTBT$. The first one yields $(4!)^2$ as does the second.
The answer is then $8!-2(4!)^2=39168$.
