A starting lineup in basketball consists of two guards, two forwards, and a center.

Now suppose the roster has 5 guards, 4 forwards, 3 centers, and 2 "swing players" (X and Y) who can play either guard or forward. If 5 of the 14 players are randomly selected, what is the probability that they constitute a legitimate starting lineup?

  1. 👍
  2. 👎
  3. 👁
  1. number of ways to choose any 5 of the 14
    = C(14,5) = 2002

    number of "legitimate" starting lineups

    1. X and Y excluded:
    C(5,2) x C(3,1) x C(4,2) = 180

    2. X plays guard, Y included in the forwards
    C(5,1) x C(5,2) x C(3,1) = 150

    3. Y plays guard, X included in the forwards
    same as #2 ---> 150

    4. Both X and Y play forward
    C(5,2) x 1 x C(3,1) = 30

    5. Both X and Y play guard
    1 x C(4,2) x C(3,1) = 18

    I will let you finish it.

    1. 👍
    2. 👎
  2. 528/2002 = 0.264 but it's wrong.

    1. 👍
    2. 👎
  3. ok jil, I forgot the case where only one of "swing players" is in the lineup

    6. X plays guard, Y does not play
    C(5,1) x 1 x C(4,2) x C(3,1) = 90

    7. X plays forward, Y does not play
    C(5,2) x 1 x C(4,1) x C(3,1) = 120

    We have the same cases if Y plays, but not x

    so the total of all exceptions
    = 180 + 2(150) + 30 + 18 + 2(90+120) = 948

    prob = 948/2002 = .4735

    How does that look?

    1. 👍
    2. 👎
  4. 180+150+150+30+18+90+120 = 738/2002 = .3686

    1. 👍
    2. 👎
  5. Both answers of 0.4735 and 0.3686 are wrong. We got 768 cases, 0.3836, still wrong.

    1. 👍
    2. 👎
  6. My answer is different

    Legitimate lineup when both x and y are guards comes out to be 3c1*7c2*5c2=630

    Similar would be the case when both are forwards

    Also when one is forward and one is guard ,no. Of ways are (3c1*6c2*6c2)*2 since their positions are interchangeable

    Total ways= 2610

    Ways of selecting 5 out of 15 players = 15c5 = 3003

    Required probability is 2610/3003=

    Is this the correct answer?

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    Our school's girls volleyball team has 14 players, including a set of 3 triplets: Missy, Lauren, and Liz. In how many ways can we choose 6 starters if the only restriction is that not all 3 triplets can be in the starting lineup?

  2. Math

    Marcus plays basketball for nine hours each week his friend Louis spends 5/6 as much time playing basketball who plays more basketball? I think you multiply 9x5/6, is that correct?

  3. Bubbles

    starting from 105 feet away a person on a bicycle rides towards a checkpoint and then passes it. the rider is traveling at a constant rate of 35 feet per second. THe distance between the bicycle and the checkpoint is given by the

  4. physics

    From a height of 2.15 m above the floor of Boston's Fleet Center, forward Paul Pierce tosses a shot straight up next to the basketball hoop with a KE of 5.40 J. If his regulation-size. basketball has a mass of 0.600 kg, will his

  1. math

    110 members of a sports club play at least one of the games, football, basketball and volleyball. If 20 play football and basketball only,15 play football and basketball only, 26 play basketball and volleyball only,x play all the

  2. math

    My soccer team has 16 players. I have to choose a starting lineup of a goalie and 10 regular players (the regular players are interchangeable). How many different starting lineups can I choose?

  3. Math

    18 students in a class play baseball. 17 students in the class play basketball. 30 students in the class play either or both sports. Select the vend diagram that shows the number of students who play basketball and baseball. A.

  4. Math

    The diameter of a basketball rim is 18 inches. A standard basketball has a circumference of 30 inches. What is the distance between the ball and the rim in a shot in which the ball goes exactly in the center of the rim? Show your

  1. Physics

    Suppose that a simple pendulum consists of a small 66.0 g bob at the end of a cord of negligible mass. Suppose that the angle between the cord and the vertical is given by θ = (0.0800 rad) cos[(4.30 rad/s)t + ϕ] (a) What is the

  2. Math

    Lee is running around the perimeter of a circular track at a rate of 10 ft/sec. The track has a radius of 100 yards. After 10 seconds, Lee turns and runs along a radial line to the center of the circle. Once he reaches the center,

  3. Math

    A community center has 3 tennis teams and 5 basketball teams. No one is on both teams. How many athletes are there? Tennis---2 players Basketball---5 players Softball---10 players

  4. Economics/Marginal Analysis

    21st Century Electronics has discovered a theft problem at its warehouse and has decided to hire security guards. The firm wants to hire the optimal number of guards. The follwoign table shows how the number of security guards

You can view more similar questions or ask a new question.