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, four guards, five forwards, and one individual (X) who can playeither guard or forward. How many different starting lineups can be created? [Hint: Consider lineups without X, thenlineups with X as guard, then lineups with X as forward.]lineups(b) Now suppose the roster has 3 guards, 4 forwards, 3 centers, and 2 "swing players" (X and Y) who can play eitherguard or forward. If 5 of the 12 players are randomly selected, what is the probability that they constitute a legitimatestarting lineup? (Round your answer to three decimal places.)

Answered: Image /qna-images/answer/5df241a2-45e3-4a46-a067-02a8bc1ea9f8.jpg

Answered: A starting lineup in basketball…

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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In a survey of 500 students in a university, 200 are enrolled in Math, 180 are enrolled in Chemistry, 170 are enrolled in Physics, 40 in Math and Chemistry, 45 in Chemistry and Physics, 50 in Math and Physics, and 15 in all the three courses. How many students are enrolled in: a. any of the three coursesb. Neither of the three coursesc. Not in Math or not in Physicsd. Not in both Math and Physicse. Physics but not in Mathf. Math and either Physics or Chemistryg. Math and Physics or Math and Chemistry
Consider a 6 vs 6 youth soccer team (i.e., teams field 6 players at once) with 9 players. (a) How many different combinations of players can the team field? (b) If the team has exactly one goalie (who has to play), how many different combinations of players can the team field? (c) If the team has exactly two goalie (exactly one of which has to play and the other cannot), how many different combinations of players can the team field?
Andy and Marjorie are playing tennis. The points system is as follows: there are two conditions for a player to win a game: 1) A player must reach four points in that game before their opponent. So for example, if Andy wins four out of the first five points, then he wins 4-1. 2) A player must have at least two more points in that game than their opponent. So for example, if the score is 3-3 and then Andy wins a point, then the score is 4-3 to Andy but the game isn't over. If Andy wins the next point, then he wins the game 5-3; otherwise, the score is 4-4, and again a player must win two points in a row to win the game. When the score in a game is tied at 3-3 (or 4-4, or 5-5, and so on), it is called 'deuce'. To win a set, a player must win six games before their opponent and as with games, this must be by a difference of two. So for example if Marjorie wins 6 out of the first 8 games, she wins the set 6-2. Unlike games, however, sets do not go on indefinitely. You may assume for now…
. Among a group of 100 book enthusiasts: 40 people like mystery novels, 60 like science fiction novels, 30 likeromance novels, and 10 like both mystery and romance novels. While all surveyed liked at least one genre ofnovel, it has been established that none of the people like both science fiction and romance novels. Howmany people like both mystery and science fiction novels?
Packages arrive at the stockroom and are delivered on carts to offices and laboratories by student employees. The carts and packages are various sizes and shapes. The students are paid according to the carts used. There are 6 carts and the pay for their use is Product C1: $1 Product C2: $3 Product C3: $2 Product C4: $4 Product C5: $1 Product C6: $2 On a particular day, 9 packages arrive, and they can be delivered using the 6 carts as follows: C1 can be used for packages P1, P3, P4 and p7. C2 can be used for packages P2, P5, and P6, and p8. C3 can be used for packages P1, P2, P5, P6, and P7. C4 can be used for packages P3, P6, and P7 and 9. C5 can be used for packages P2, P4 and p8. C6 can be used for packages P1, P2 and P3 The stockroom manager wants the packages delivered at minimum cost. Using minimization techniques described in this unit, present a systematic procedure for finding the minimum cost solution. Use Petrik Method
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A twenty-something single person is planning a ski vacation. Assume that he has 2 possible destinations: Utah, and Oregon. There are 4 ski areas in Utah with 4 available times for 3 of the areas, and 1 times for the other area. There are 4 ski areas in Oregon with 2 available times for 3 of the areas, and 4 times for the other area. (A "time" refers to a weekend for which there are vacancies at the ski lodge.) A trip plan involves the selection of a location, ski area, and a time. How many possible plans are there?
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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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