Question

A gardener has three flowering shrubs and four nonflowering shrubs, where all shrubs are distinguishable from one another. He must plant these shrubs in a row using an alternating pattern, that is, a shrub must be of a different type from that on either side. How many ways can he plant these shrubs? If he has to plant these shrubs in a circle using the same pattern, how many ways can he plant this circle? Note that one nonflowering shrub will be left out at the end.

Answer 1

Answer:

Either way you can in 144 ways.

Step-by-step explanation:

According to the statement we have 3 flowering shrubs and 3 flowerless shrubs.

We name them as follows:

S = flowering shrub

N = non flowering shrub

Now the only pattern in which these bushes can be arranged alternately  as follows:

N-S-N-S-N-S-N

Therefore, to calculate the number of forms it would be:

Number of shapes: 4 * 3 * 3 * 2 * 2 * 1 * 1 = 144

Which means there are 144 ways.

Now if we organize them in a circle in the same way

again it would be the same number of ways to organize them: 144 ways.

This is because the nun's last blooming shrub is left outside.