How many ways can you choose a manager and assistant from a 9-person task force?
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- A financial institution, Kumpannee, has two departments. Department A has 8 individuals and Department B has 9 individuals. Kumpannee needs to select a team of 5 individuals to produce a forecast on the price of a barrel of crude oil. How many different teams are possible if at most 1 team member should come from Department A? O a. 18,144 ОБ.1,134 O c. 579 O d. 39,312 e. 25238) SET UP ONLY: A business has 3 machines that manufacture containers. Together they can make 100 containers per day, whereas the two fastest machines can make 80 containers per day. The fastest machine makes 34 more containers per day than the slowest machine. How many containers can each machine make per day?1. Read and analyze the following problems. Write your solution on a sheet of paper. The coach of the winning basketball team chooses 3 of the 15 members to be interviewed by a sports reporter. In how many ways can the members to be interviewed be chosen? A poker hand consists of 5 cards chosen at random from a standard deck of cards. How many poker hands containing all face cards are possible? 2. 3. Suppose 7 female and 6 male applicants have been successfully screened for 5 positions. In how many ways can the following compositions be selected? a. 5 people regardless of gender b. 3 females and 2 males C. at least 3 females d. 4 females and 1 male e. 5 females 4. In a game of poker, a full house is a combination of 5 cards chosen from a standard deck of cards with three of a kind and two of a kind. How many full houses are possible?
- You work at McKinsey Company and you are in charge of assigning 6 new consultant analysts to projects. There are 5 projects in total. For a given project, up to 3 new consultants can be assigned (i.e., either 0,1,2 or 3 consultants will be assigned to each project). Each consultant is assigned to exactly one project. The table below indicates on which projects the new consultants can be assigned based on their skills and areas of expertise. Project A Project B Project C Project D Project E Consultant 1 Yes Yes Yes No Yes Consultant 2 No Yes No No Yes Consultant 3 Yes No No Yes Yes Consultant 4 Yes Yes Yes Yes No Consultant 5 Yes…You are coaching a high school basketball team and you realize the importance of free throw shooting, the skill to make foul shots. The question is: how much practice time should be spent in shooting free throws. Thus, you divide your team of 21 players into three groups and practice according to the following schedule that produces thee results after one month. The results are the number of free throws made in 50 attempts. 10 minutes per practice session 15 minutes 20 minutes 25 26 34 30 32 33 31 30 32 33 32…