+0  
 
+1
397
1
avatar

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?

 Apr 5, 2021
 #1
avatar+605 
+1

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 $8!-2(4!)^2=39168$.

 Apr 5, 2021

4 Online Users

avatar
avatar