A group of nine people are attending the movies together. (a) Two of the nine insist on sitting side-by-side. In how many ways can the nine be seated together in a row? (b) Two of the people do not like each other and do not want to sit side-by-side. Now how many ways can the nine be seated together in a row?

A group of nine people are attending the movies together. (a) Two of the nine insist on sitting side-by-side. In how many ways can the nine be seated together in a row? (b) Two of the people do not like each other and do not want to sit side-by-side. Now how many ways can the nine be seated together 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

Eight freshmen and eight sophomores want to play flag football. At URI, a flag foot- ball team must have exactly eight members. For this problem, you may leave your answers unreduced. (a) How many teams can be chosen that contain four freshmen and four sophomores? (b) How many teams can be chosen that contain at least two sophomores? (c) How many teams can be chosen that contain at most two freshmen?
6 people consisting of 3 couples are seated in a row of 6 chairs to take group pictures.(a) In how many ways could they be seated?(b)How many ways could they be seated if each couple should sit next to each other?Justify your answer.(c) One of the couples broke up and do not want to sit next to each other. Whereas the other 4 want to sit next to their partners. In how many ways could they be seated?
Jack packs 3 pairs of shoes, 4 pairs of boots, 8 pairs of jeans, 9 pairs of dress pants, and 2 dress shirts for a trip. (a) How many different outfits can Jack make with these items? (b) If Jack were to bring along 4 sweaters so that he could wear either a dress shirt or a sweater or he could wear both a dress shirt and a sweater, how many outfits could Jack make? (a) Jack can make (Type a whole number.) different outfits with these items. (b) Jack can make different outfits with these items. (Type a whole number.)
(a) Mrs. Ruiz has 15 boys and 12 girls in her class. In how many ways can she select a committee to organize a class party if the committee must contain 2 boys and 2 girls? (b) Lourdes, a girl, and Andy, a boy, always fight. How many ways can Mrs. Ruiz select the committee of part (a) if she does not want both Lourdes and Andy on the committee? Note that Lourdes can be on the committee, and Andy not on the committee, or vice versa.
A math instructor has 35 calculators in her office. Of them, 17 have dead batteries, 13 have cracked displays, and 22 have missing buttons. Of those with dead batteries, 5 have cracked displays and 11 have missing buttons. Of those with cracked displays, 8 have missing buttons. There are 3 with dead batteries, cracked displays, and missing buttons. How many calculators does she have with nothing wrong with them? (A) 4 (B) 6 (C) 3 (D) 7 (E) 8 (F) 2 (G) 1 (H) 9 O A OB OC OD OE OF H.
Q4. A group of students: Saif, Al Mohanned, Abdullah, Rihab, Shahad, Manar, Thuwaiba, Lamees, and Taqwa walk into a class room which has a table with only 6 chairs. In how many ways can they be seated on the available chairs if order is important.
You break your piggy-bank to discover lots of pennies and nickels. You start arranging these in rows of 6 coins. a. You find yourself making rows containing an equal number of pennies and nickels. For fun, you decide to lay out every possible such row. How many coins will you need? b. How many coins would you need to make all possible rows of 6 coins (not necessarily with equal number of pennies and nickels)?
Last Super Bowl weekend, there were 109 pizzas ordered for the sophomore dorm. That weekend 32 customers ordered their pizza with just pepperoni, 40 ordered their pizza with just sausage, 18 ordered theirs with just onions, 13 ordered theirs with pepperoni and sausage, 10 ordered theirs with sausage and onions, 9 ordered theirs with pepperoni and onions, and 7 ordered theirs with all three items. (a) How many customers ordered their pizza with pepperoni or sausage (or both)? (b) How many customers ordered their pizza with sausage or onions (or both)? (c) How many customers ordered a pizza without pepperoni, sausage, or onions?
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)
There are 53 students. Of these, 25 are taking Business, 26 are taking English, and 25 are taking Math. 14 are taking both Business and Math, 13 are taking Math and English, and 17 are taking Business and English. 12 students are taking none of these three classes. How many students are taking Business but are not taking Math?
At a elementary school graduation party 4 girls, 2 boys, and 1 teacher have to be arranged in a row. In how many ways can this be done if: (a) they can be arranged in any order? Answer: (b) the boys must be together and the girls must be together? Answer: (c) the boys must be together but the others can be arranged in any order? Answer:
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?