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# help counting

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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

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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