A starting lineup in basketball consists of two guards, two forwards, and a center.(a) A certain college team has on its roster four centers, five guards, four forwards, and one individual (X) who can play either guard or forward. How many different starting lineups can becreated? [Hint: Consider lineups without X, then lineups with X as guard, then lineups with X as forward.]lineups(b) Now suppose the roster has 5 guards, 5 forwards, 4 centers, and 2 "swing players" (X and Y) who can play either guard or forward. If 5 of the 16 players are randomly selected, what is theprobability that they constitute a legitimate starting lineup? (Round your answer to three decimal places.)

The given problem can be solved using 'combination'. Combination is used when the order in which…

Answered: A starting lineup in basketball…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A. A company manufactures three goods, X; Y and Z, each of which is made from three types of input, A; B and C. Each unit of X requires 1 unit of A, 7-units-of- B and 3 units of C. Each unit of Y requires 4 units of A, 3 units-of-B-and-1 unit. of C. Furthermore, one unit of Z-requires 2 units of A, 4 units of B and 2 units. of C. In a particular day's production the company uses up 105 units of A, 135. units of B and 55 units of C. ¶ i. → Create an augmented matrix to represent the usage of A; B-and-C-in-the- day's production of x; y-and-z-units of X; Y and Z.respectively. 1 ii. → Using Row reduction method, determine the values of x; -y-and-z. → 1 ¶ B.-Express the following system of equations in matrix form and solve it using. (elementary row operations) row reduction matrix method. -3x + y + z = 11 -x+y=z= -11 -5r+v+z = 3¶
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?
A student works in a bookstore where he is required to work at least four and at most five days a week, at least one of which has to be a weekend day (Saturday or Sunday). How many different weekly work schedules can this student have?
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?
Which of the following could be the number of players on each team?
Radar detectors are either powered by their own battery or plug into the cigarette lighter socket. All radar detectors come in three models: no-frills, standard, and fancy. In addition, detectors powered by their own batteries detect either radar or laser, or both, whereas the plug-in types come in models that detect either radar or laser, but not both. How many different radar detectors can you buy? ------------------------------------ choices
A bag contains five red marbles, three green ones, one lavender one, three yellows, and two orange marbles. HINT [See Example 7.] How many sets of four marbles include none of the red ones?
A company is organizing a team-building event with various activities. There are 12 employees attending the event, and they need to be split into three teams: Team A, Team B, and Team C. Each team should have at least 2 members but no more than 6 members. In how many different ways can the teams be formed? (Note: The order of the teams doesn't matter; i.e., Team A, Team B, and Team C is the same as Team C, Team A, and Team B.)
A starting lineup in basketball consists of two guards, two forwards, and a center. a. A certain college team has on its roster three centers, four guards, four forwards, and one individual (X) who can play either guard or How many different starting lineups can be created? [ Hint. Consider lineups without X, then lineups with X as guard, then lineups with X as forward.] b. Now suppose the roster has 5guards, 5 forwards, 3 centers, and 2 "swing players"(X and Y) who can play either guard or forward. If 5 of the 15 players are randomly selected, what is the probability that they constitute a legitimate starting lineup?

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