Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate notation: ( ) For Questions 10: A panel of 4 Democratic candidates, 4 Republican candidates, and 2 Independent candidates will participate in a political forum. 10.) (a) How many ways are there to randomly select 3 featured speakers from the panel to introduce 3 different topics of discussion during the event? (b) In how many ways can the candidates be seated in a row on the stage if the Democrats will be seated together, the Republicans will be seated together, and one independent can

Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate notation: ( ) For Questions 10: A panel of 4 Democratic candidates, 4 Republican candidates, and 2 Independent candidates will participate in a political forum. 10.) (a) How many ways are there to randomly select 3 featured speakers from the panel to introduce 3 different topics of discussion during the event? (b) In how many ways can the candidates be seated in a row on the stage if the Democrats will be seated together, the Republicans will be seated together, and one independent can

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 math instructor has 46 calculators in her office. Of them, 22 have dead batteries, 28 have cracked displays, and 24 have missing buttons. Of those with dead batteries, 16 have cracked displays and 11 have missing buttons. Of those with cracked displays, 18 have missing buttons. There are 9 with dead batteries, cracked displays, and missing buttons. How many calculators does she have with nothing wrong with them? (A) 6 (В) 4 (C) 5 (D) 9 (E) 8 (F) 3 (G) 1 (H)
You have one pile of 11 building blocks, each one a different color, and you also have another pile of 7 blocks, again each one a different color. How many ways are there to build a tower 4 blocks high from the first pile and another tower 3 blocks high from the second pile? Assume that the colors at each level of a tower matter. (A) 318 (B) C(11,4) C(7, 3) (C) P(11,4) P(7,3) (D) P(18,7) (E) 311 (F) C(18,7) (G) P(11,4)+ P(7,3) (H) C(11,4)+ C(7,3) O A OB OC O E O F OG H.
Suppose there are 5 men and 8 women qualified to be members of a new committee of 6 people, includinga president, a vice-president, and a secretary.(a) How many different ways do you have to pick a president, vice-president and secretary if you need atleast 1 men and 1 women? Does the order matter? Why?(b) How many different committees can you form with at least 3 women? Does the order matter? Why?
An instructor gives an exam with twenty questions. Students are allowed to choose any fifteen questions to answer. (a) How many different choices of fifteen questions are there? (b) Suppose nine questions require coding and eleven do not. (i) How many groups of fifteen questions contain seven that require coding and eight that do not? (ii) How many groups of fifteen questions contain at most eight that require coding? (c) Suppose the exam instruction specifies that at most one of questions 1 and 2 MAY BE included among the fifteen. How many different choices of fifteen questions are there? (d) Suppose the exam instruction specifies that either both questions 1 and 2 are to be included among the ten or neither is to be included. How many different choices of ten questions are there?
A bagel shop has a selection of 8 different kinds of bagels (at least 10 of each). (.1) How many different selections of 10 bagels can be made? ( .2) If garlic is one kind of available bagel and onion is another, how many different selections of 10 bagels can you make so that you have at least 3 onion bagels and exactly 2 garlic bagels?
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
Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate notation: ( ) 17.) A hand of 5 cards is dealt in a poker game. How many poker hands are possible with: (a) exactly 3 Jacks? (b) only one color (red or black)? (c) a full house (3 of one kind of card and 2 of another)?
Determine the "n" and "p" in the following problems and write them in Combination notation. a)Abag contains 4 white balls, 6 yellow balls, and 5 red balls. In how many ways can 6 balls be chosen if there must be 2 balls of each color? b) If 4 marbles are picked randomly from a basket containing 5 blue marbles and 8 yellow marbles, in how many ways can it happen that at least 3 of the marbles picked are blue? c)There are 7 men and 9 women members of a club. How many committees of 4 can be formed having at most 3 men?
There are 22 members of a basketball team. (1) The coach must select 8 players to travel to an away game. How many ways are there to select the players who will travel? (2) From the 8 players who will travel, the coach must select her starting line-up. She will select a player for each of the five positions: center, right forward, left forward, right guard, left guard. How many ways are there for her to select the starting line-up? (3) From the 8 players who will travel, the coach must select her starting line-up. She will select a player for each of the five positions: center, right forward, left forward, right guard, left guard. However, there are only 3 of the 8 players who can play center. Otherwise, there are no restrictions. How many ways are there for her to select the starting line-up?
There are 25 applicants for four jobs; Computer Programmer, Software Tester, Manager, and Systems Engineer. This is an example of [Select] n= [Select] r = [Select] There are [Select] ways to choose an applicant for the positions of a computer programmer, software tester, manager, and systems engineer.
A basket contains 2 pink, 3 yellow, 8 red, and 1 black jelly beans. You grab a handful of 4 jelly beans. (a) How many groups of 4 jelly beans include exactly 1 of each color? (b) How many groups of 4 jelly beans include at most 1 yellow?