How many ways can the 16 players be distributed into iwo teams of 8 players such that Oski and the tree arc in opposite teams?

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

the preceding players. Let 1-8 represent the players’ heights. An example of a valid ordering:

4. 5.6.3, 2.7. 1, 8. An example of an invalid ordering: 1,2. 3.4.5, 6,8.7. (invalid since 7 is neither taller nor shorter than all the preceding players). How many such orderings exist?

(d) To keep viewership up after the tournament finishes, the council plans an All-Star match. The 16 greatest players in the league were chosen. including Oski and a tree..? Oski refuses to play on the same team as the tree. How many ways can the 16 players be distributed into iwo teams of 8 players such that Oski and the tree arc in opposite teams?

(e) Provide an explanation for the following combinatorial identity. Hint: Solve the previous pan using another method. Those two methods should correspond to the two sides of the equality.

(n\r) (n-2’\ r—2)(n-2’/r)=(n-2/r-1)

5 School Carpool

(a) n males and n females apply to EECS within UC Berkeley. The EECS department only has,seats available. In how many ways can it admit students? Use the above story for a combina.

tonal argument to prove the following identity:

(b) Among the n admitted students, there is at least one male and at least one female. On the first day, the admitted students decide to carpool to school. The male(s) get in one car, and the

female(s) get in another car. Use the above story for a combinatorial argument to prove the following identity:

(Hint: Consider the ways that students are admitted. Also, each car has a driver!)

6  Coins

Suppose we have an unbiased coin, with outcomes H and T, with probability of heads P[H] = 1/2 and probability of tails also P[T] = 1/2. Suppose we perform an experiment in which we toss the

coin 3 times. An outcome of this experiment is (X, ,X2.X3), where X, € {H, T}.

(a) What is the sample space for our experiment?

(b) Which of the following are examples of events? Select all that apply.

. {(H,H,T)(H.H),(T))

Attachments:

Related Questions

. The fundamental operations of create, read, update, and delete (CRUD) in either Python or Java

CS 340 Milestone One Guidelines and Rubric  Overview: For this assignment, you will implement the fundamental operations of create, read, update,

. Develop a program to emulate a purchase transaction at a retail store. This  program will have two classes, a LineItem class and a Transaction class

Retail Transaction Programming Project  Project Requirements:  Develop a program to emulate a purchase transaction at a retail store. This

. The following program contains five errors. Identify the errors and fix them

7COM1028   Secure Systems Programming   Referral Coursework: Secure

. Accepts the following from a user: Item Name Item Quantity Item Price Allows the user to create a file to store the sales receipt contents

Create a GUI program that:Accepts the following from a user:Item NameItem QuantityItem PriceAllows the user to create a file to store the sales receip

. The final project will encompass developing a web service using a software stack and implementing an industry-standard interface. Regardless of whether you choose to pursue application development goals as a pure developer or as a software engineer

CS 340 Final Project Guidelines and Rubric  Overview The final project will encompass developing a web service using a software stack and impleme