6. II have to invite 7 out of my 14 friends to a party. In how many ways can I do that ifa. Both of my friends Abu and Deps will be part of the group?b. Only one of them will be part of the group?c. None of them will be part of the group?

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Answered: 6. I I have to invite 7 out of my 14…

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...

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3. The students' council is having pizza at their next meeting. There are 20 council members, 6 of whom are vegetarian. A committee of 3 will order six pizzas from a pizza shop that has a special price for large pizzas with up to three toppings. The shop offers ten different toppings. a) How many different pizza committees can the council choose if there must be at least one vegetarian and one non-vegetarian on the committee?
At a music festival, there are seven bands scheduled to play, numbered 1 through 7. a. How many different ways can these bands be arranged to perform? b. If band 3 is performing first and band 1 last, then how many ways can their appearances be scheduled? a. There are different ways to arrange the bands. (Simplify your answer.) b. If band 3 is performing first and band 1 last, there are different ways to arrange the bands. (Simplify your answer.) Enter your answer in each of the answer boxes.
11. Consider 14 books: 6 Science, 5 Math, 3 English, to be arranged in a book shelf where only 7 books can be placed. How many ways a. Can one arrange with more than 4 Science books? b. Can one arrange with at least 2 Math books? Can one arrange without English books? C.
1. Remove any three red and any three blank cards from the deck for both you and your friend. You will each have six cards. 2. Shuffle the remaining cards in the deck.
The College of Engineering (CEA) School Body (SB) is looking for a new President and secretary for the incoming school year. 50 candidates applied for the position. How many different choices of the officers are possible if a. There are no restrictions b. Student A will serve only if he is chosen as president. c. Student B and C will serve together or not at all d. Student D and E will not serve together
4) A box contains 5 green, 7 yellow & 10 orange pingpong balls. How many ways can 5 balls be selected if: a. all the balls are orange? b. all the balls are green? c. all the balls are yellow? d. 2 are orange & 3 are yellow? e. 1 is green & 4 are orange?
you are planning a wedding, and there are 10 people participating in the weddingceremony.1. During the ceremony, the 10 participants will walk down the aisle in pairs (groupsof 2), one pair at a time. How many ways can the 10 participants walk down theaisle in pairs if it matters which person is on the left and which is on the right?2. After walking down the aisle and completing the wedding ceremony, the 10 parti-cipants will leave the ceremony in pairs. How many ways can the 10 people leavethe ceremony in pairs, one pair at a time, if the left and right orientation of eachpair is now irrelevant?3. After leaving the ceremony there is a reception held where the 10 wedding parti-cipants will dance together. How many ways can the 10 participants form pairswhile dancing at the same time?
2. If there are 120 people in your college class, are there at least 5 people that share the same last initial? a. Let the pigeon holes be: b. Let the pigeons be: c. What is k? d. Now the number of pigeons would have to be greater than: e. Is the number of pigeons or people greater? Why or why not? f. Are there at least 5 people that share the same last initial if there are 120 people in the college class? Why or why not? Write your response below:
15) Use the situation below to answer the question that follows. Team Jet has 7 members who won a school competition. Of these 7, 4 members are randomly picked to receive prizes for winning. The 1st member selected wins a $50 gift card; the 2nd person selected wins a $25 gift card; the 3rd person selected wins a $10 gift card; the 4th person selected wins a $5 gift card. The names of Team Jet's members are represented by the first letter of their first names, as displayed in the following table: Name Frank Gina Harriet Inez Jakob Keven Liu Letter F G H I J K L In the box below, complete the remaining three rows of the list that models how to calculate the number of possible ways 4 team members can be selected to win the prizes. 1) FGHIJKL Let Lui win the 1st prize, so select L. 2) 3) 4)
In a UC student club, a president and treasurer are to be chosen consisting of 45 people. a. How many different choices of officers are possible if there are no restrictions? b. How many different choices of officers are possible if A will serve only if he is president? c. How many different choices of officers are possible if B and C will serve together or not at all. d. How many different choices of officers are possible if D and E will not serve together?

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6. I I have to invite 7 out of my 14 friends to a party. In how many ways can I do that if a. Both of my friends Abu and Deps will be part of the group? b. Only one of them will be part of the group? c. None of them will be part of the group?