Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate notation: ( ) For Question 11: A panel of 4 Democratic candidates, 4 Republican candidates, and 2 Independent candidates will participate in a political forum. 11.) If members of each party do not need to be grouped together, and we consider candidates from the same party (as well as Independents) as indistinguishable, in how many distinguishable ways can the candidates be seated in a row?

Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate notation: ( ) For Question 11: A panel of 4 Democratic candidates, 4 Republican candidates, and 2 Independent candidates will participate in a political forum. 11.) If members of each party do not need to be grouped together, and we consider candidates from the same party (as well as Independents) as indistinguishable, in how many distinguishable ways can the candidates be seated in a row?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

A large research project is looking for more researchers. There are 8 spots open on the research team. There are 10 mathematicians and 14 computer scientists that apply for the team. a. How many different ways can a team of 8 be made for the project? b. How many different ways can a team of 8 be made for the project if the team must contain at least one computer scientist and at least one mathematician.
An experiment is designed to see whether 3rd graders can write faster with a pen or pencil. Four third graders participate, 2 boys and 2 girls. For each child, a marble is drawn without replacement from a bucket containing 2 red marbles and 2 blue marbles. If a red marble is selected, the child gets a pen and if blue, the child gets a pencil. The children are assigned in this order: boy 1, girl 1, boy 2, girl 2. LetX be the number of boys assigned to a pen. Find E (X). Find SD(X). а. b.
Suppose that Jeremy is a highschool science teacher and that he is dividing 16 students in his advanced chemistry class into four groups of four for a lab activity. Each of the four lab groups has been assigned its own task to complete for the activity, but the students are not assigned specific roles within the group. How many different ways can Jeremy assign his students to the four lab groups?
Jessica is grocery shopping and has 16 cherry tomatoes and 12 grape tomatoes in her shopping basket. When she gets home, she prepares her ingredients for lunch, but she forgets which of the tomatoes are cherry and which are grape. She cannot distinguish between the two types of tomatoes, so she just picks 13 tomatoes. How many different sets of 13 tomatoes are possible if there are exactly 7 cherry tomatoes?
In the local boating pond there are 10 plain wooden boats, each with a different number. The owner decides that some of these boats will be painted: one in blue, one in green, one in red, and one in orange, and the remaining ones left unpainted. How many ways are there to paint the boats? The number of ways is
You are going to a bakery and they are selling bread (B), doughnuts (D) and cookies (C). A. If you are only going to buy two different items, list all of the permutations. B. If you are only going to buy two different items, list all of the combinations.
d. [Permutation] Solve the following problems - Find the number of words that can be formed by using the letters of the word "DEMOCRACY" where first letter will be always C and last letter will be R. e. [Combination] A group of 15 students is to be formed from 44 students of MATI00 Course. Among the students of the course there is 2 renowned batsmen, 3 spinners, 2 fast blowlers and 2 wicketkeepers. How many different ways this can be done so as always to (i) include 1 renowned batsman, 1 fast bowler, 1 spinner and 1 wicketkeeper; and (ii) exclude spinners? 2.
During a special promotion, a customer purchasing a computer and a printer is given a choice of 3 free software packages. There are 10 different software packages from which to select. How many different groups of software packages can be selected? Hint: This is a Combination problem! 120 604,800 360 720
Try to look for a playing card if available then observe. If not, you can read the description to be able to solve the word problems that will follow. Playing cards: A deck of playing cards has 52 cards: • Labels: with one lettered card ace (A), numbered cards (2-10), and face cards king(K), Queen(Q), Jack(J) • With 4 suits: diamond (•), clubs(4), spades(a) and hearts(♥) two colors: red cards and black cards POKER HANDS ROYAL FLUSH STRAIGHT FLUSH FOUR OF A KIND FULL HOUSE FLUSH STRAIGHT THREE OF A KIND TWO PAIRS ONE PAIR HIGH HAND Poker Hand: Playing with 5 playing cards in hand. • Royal flush-A royal flush is an ace high straight flush. For example, A-K-Q-J-10 all of diamonds. • Straight flush- A straight flush is a five-card straight, all in the same suit. For example, 7-6-5-4-3 all of spades. Four of a kind- Four of a kind, or quads, are four cards of equal value. For example, four jacks. • Full House- A full house contains a set (3) of cards of one value and a pair of another…
If S-(0,1,2,3,4,5,6,7,8,9} and A-{0,2,4,6,8}, B={1,3,5,7,9}, C={2,3,4,5} and D={1,6,7), list the elements of C! Write the answer in the format: (A, B, C} Answer: C' = type your answer..