Question

In: Advanced Math

How many ways can a gardener plant five different species of shrubs in a circle? What...

How many ways can a gardener plant five different species of shrubs in a circle? What is the answer if two of the shrubs are the same? What is the answer if all the shrubs are identical?

Expert Solution

Let be the different species of shrubs to be planted in five different places on a circle.

has five choices to get planted. has four choices, has three, has two and has only one choice to get planted. So, total number of structures (with repetition) we get on a circle is . But here, every structure is repeated times. So the total number of different structures i.e. number of ways of planting these shrubs on a circle is .

Now, suppose two shrubs, say and , where , are of the same species. So any two structures with and interchanging their places will be the same. Therefore Number of ways in this case is .

When all the shrubs are the same, naturally there is only one way to plant them on a circle.

Colby Messinger answered 2 years ago

10 people are sitting in a circle. How many different ways can they be seated relative...

10 people are sitting in a circle. How many different ways can they be seated relative to each other if Steve and Alice must be seated directly across from each other? Do I need to apply the circular permutation formula of (n-1)!, and do I need to multiply the end result by 2 to account for the fact that they could be in different positions kinda like standing beside each other where one is on the left but could also...

7. How many different ways can the letters in “COUNT” be arranged? 8. How many different...

7. How many different ways can the letters in “COUNT” be arranged? 8. How many different ways can the letters in “PROBABILITY” be arranged? 9. A pizza restaurant offers 15 different toppings, but only allows customers to select up to four different toppings for each pizza. How many different ways are there for customers to choose up to four toppings for a pizza? 10. A youth soccer team consists of 12 players. When they have games, they play simultaneously on...

How many ways a team of five salespersons can be formed from a group of 10...

How many ways a team of five salespersons can be formed from a group of 10 salesmen and 8 saleswomen, if the team contains at most 2 saleswomen?

In how many ways can a five horse race end, allowing for the possibility that two...

In how many ways can a five horse race end, allowing for the possibility that two horses tie?

What are five ways Cox and DuBois are different?

If there are 1296 different ways that 4 (6 sided) dice can be rolled, how many...

If there are 1296 different ways that 4 (6 sided) dice can be rolled, how many of the 1296 possibilities have less than 2 fives rolled?

(a) In draw poker, how many ways can you get a full house? (a five card...

(a) In draw poker, how many ways can you get a full house? (a five card hand with 3 of one number and 2 of another number) (b) How many 7-digit telephone numbers exist? (c) How many 7-digit telephone numbers exist where no number is repeated? (d) How many 7-digit telephone numbers exist where the last 3 digits are 911? (e) How many 7-digit telephone numbers exist for a given area code if the sequence 911 can’t occur? (e.g. 838-9115...

For each of the following five reactions, circle the specific chemical species that is: reduced, and...

For each of the following five reactions, circle the specific chemical species that is: reduced, and draw a box around the specific chemical species that is oxidized: a) MnO2 (s) + 2 I- (aq) +4 H+ (aq) --> Mn2+ (aq) + I2 (aq) + 2 H2O (l) b) Cd (s) + 2 NiO(OH) (s) + 2 H2O (l) --> 2 Ni(OH)2 (s) + Cd(OH)2 (s) c) NH4+ (aq) + 2 O2 (g) --> NO3- (aq) + 2 H+ (aq) +...

What are some ways that new species can arise? Describe how natural selection can lead to...

What are some ways that new species can arise? Describe how natural selection can lead to evolution. What are genes and genetic diversity? What is the relationship between genes and evolution?

What is a keystone species and how are they different from foundation species? What is the...

What is a keystone species and how are they different from foundation species? What is the difference between primary and secondary succession? Explain in detail. How does the Biomass Accumulation Model describe succession of ecosystems following disturbances?