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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telephone numbers in particular area consist of a three-digit area code followed by a seven- digit local number. Suppose neither the ﬁrst digit of an area code nor the ﬁrst digit of a local number can be a zero but that all other choices are acceptable. How many different area codes are possible? For a given area code, how many local telephone numbers are possible? How many telephone numbers are possible?
Suppose that Jeremy is a highschool science teacher and that he is dividing 16 students in his advanced chemistry class into four groups of four for a lab activity. Each of the four lab groups has been assigned its own task to complete for the activity, but the students are not assigned specific roles within the group. How many different ways can Jeremy assign his students to the four lab groups?
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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?
In an animal shelter, 100 cats and 50 dogs are being accommodated. Table below shows age group of the cats and dogs а. Dogs Cats Total Old 40 70 110 Young 10 30 40 Total 50 100 150 b. In a smaller animal shelter, 12 cats and 5 dogs are being accommodated. Table below shows age group of the cats and dogs. Dogs Cats Total Old 4 7 11 Young 1 5 6 Total 12 17 Why are there more old animals in shelters than young ones?
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Suppose that A E Mmxn(R) is a matrix of user ratings of various movies (on a scale of 1 to 5). Suppose we have computed the SVD of А, and decided to keep the 10 largest singular values as the most important determining factors for a user's choice of movie. Suppose also that a new user has joined the movie subscription service, and has rated some, but not all, of the movies. To predict how this new user will rate other movies (and thus, to determine which ones to recommend), all movies the user has not watched are assigned the average rating for that movie given by all users to form a new matrix A' E M(m+1)xn(R), and the rank-10 approximation of A' is computed from its SVD. The values in the approximation to A' are taken as the predicted ratings for the new user. Given this procedure, which of the following conclusions is most correct?
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