5. Alix and Billie are collecting rocks and seashells on the beach, and in total took 12 of them. There are 4 kinds: sharp rocks, round rocks, clam shells, and spiral shells. If we do not distinguish rock/seashells of the same type how many collections are possibles: (i) with no further condition? (ii) if they want at least 4 clams and 2 spiral shells? (iii) if they want at least one of each type and at most 3 round rocks? In the end, they collected 1 round rock, 2 sharp rocks, 4 clams, and 5 spiral shells (all colorful and very distinguishable), and want to distribute their loot between the two of them. Alix is to keep 2 rocks (round or sharp) and 4 shells (clam or spiral) and Billies takes the rest. (iv) How many different partitions can they make?

5. Alix and Billie are collecting rocks and seashells on the beach, and in total took 12 of them. There are 4 kinds: sharp rocks, round rocks, clam shells, and spiral shells. If we do not distinguish rock/seashells of the same type how many collections are possibles: (i) with no further condition? (ii) if they want at least 4 clams and 2 spiral shells? (iii) if they want at least one of each type and at most 3 round rocks? In the end, they collected 1 round rock, 2 sharp rocks, 4 clams, and 5 spiral shells (all colorful and very distinguishable), and want to distribute their loot between the two of them. Alix is to keep 2 rocks (round or sharp) and 4 shells (clam or spiral) and Billies takes the rest. (iv) How many different partitions can they make?

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

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?
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?
(a) In how many ways can 4 boys and 3 girls sit in a row. (b) In how many ways can they sit in a row if the boys and girls dare each to sit together
Suppose we want to choose 7 objects, without replacement, from 11 distinct objects.(If necessary, consult a list of formulas.) (a) How many ways can this be done, if the order of the choices is taken into consideration? (b) How many ways can this be done, if the order of the choices is not taken into consideration?
Suppose we want to choose 6 objects, without replacement, from 10 distinct objects. (If necessary, consult a list of formulas.) (a) How many ways can this be done, if the order of the choices does not matter? ☐ (b) How many ways can this be done, if the order of the choices matters?
Suppose we want to choose 4 objects, without replacement, from 17 distinct objects. (a) If the order of the choices is not relevant, how many ways can this be done? (b) If the order of the choices is relevant, how many ways can this be done?
Suppose we want to choose 5 objects, without replacement, from 9 distinct objects. (a) If the order of the choices is not taken into consideration, how many ways can this be done? (b) If the order of the choices is taken into consideration, how many ways can this be done?
There are 4 vacancies on the scholarship committee at a certain university. In order to balance the men and women on the committee, 1 woman and 3 men are to be appointed. In how many ways can this be done if the following are available to serve? (a) 9 men and 8 women ways(b) 4 men and 5 women ways
6. A lead role and a supporting role are to be chosen from a drama club consisting of 40 talents. How many various choices of actors are possible if: there are no restrictions? ( (1) (ii) actor Kristoff will participate only if he is the lead role? ( (ii) actors Jess and Jet will act together or not at all? (iv) actors Keanne and Gian will not act together?
10. Your cousin loves legos. She has legos that are all the same shape and look identical except that they come in three colors: red, blue, and green. (a) In how many ways can she build a tower using exactly four blue legos and eleven red legos? Include one or two sentences to explain your answer. (The tower is built up from the ground by placing legos one on top of the other.) (b) In how many different ways can she give you a bag of 20 red, blue, and green legos to take home, with at least one of each color? Include one or two sentences to explain your answer.