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.

Question

Cloe Gallagher

Mathematics

27 May, 20:55

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.

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Answers (1)

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Vernon · Answer 1

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.