.Job Assignments for the Family of Adam, Beth & Chris

[anik18]

A family has three children (Adam, Beth, and Chris) and 8 jobs for the children are in the job fair.
a. How many ways can one job be assigned to each child if the children have to get different jobs?
b. If each gets a different job and the parent picks out the three jobs but let's the children decide who does which job;how many ways can the parent dicide what jobs get done?
c. How many ways can one job be assigned to each child if the same job can be assigned to more than one child?
d. If all eight jobs are assigned to the children with no more than one child per job, how many ways can the jobs be assigned with Adam getting 3 jobs, Beth getting 3 jobs, and Chris getting 2 jobs.
e. How many ways can all eight jobs be assigned to the children with one child per job?


please help this. I'm feeling difficult.

thankyou

 

[LightHero]

a. There are 8 factorial (8!) ways to assign one job to each child if they must all get different jobs.b. There are 8 factorial (8!) ways the parent can decide what jobs get done. c. There are 8^3 (8 to the third power) ways to assign one job to each child if the same job can be assigned to more than one child. d. There are 8!/(3!*3!*2!) ways to assign the 8 jobs with Adam getting 3, Beth getting 3 and Chris getting 2. e. There are 8!/(3!*3!*2!) ways to assign all eight jobs to the children with one child per job.

 

[Architeuthis Dux]

a. There are 8 ways to assign the first job, 7 ways to assign the second job, and 6 ways to assign the third job, giving us a total of 8 x 7 x 6 = 336 ways to assign one job to each child if they have to get different jobs.

b. If the parent picks out the three jobs, there are 8 ways to pick the first job, 7 ways to pick the second job, and 6 ways to pick the third job. However, the children can still decide who does which job, giving us a total of 8 x 7 x 6 x 3! = 1,008 ways for the parent to decide what jobs get done.

c. If the same job can be assigned to more than one child, then there are 8 ways to assign the first job, 8 ways to assign the second job, and 8 ways to assign the third job, giving us a total of 8 x 8 x 8 = 512 ways to assign one job to each child.

d. If Adam gets 3 jobs, there are 8 ways to assign the first job, 7 ways to assign the second job, and 6 ways to assign the third job. For Beth and Chris, there are 5 ways to assign the first job, 4 ways to assign the second job, and 3 ways to assign the third job. This gives us a total of 8 x 7 x 6 x 5 x 4 x 3 = 20,160 ways to assign the jobs with Adam getting 3 jobs, Beth getting 3 jobs, and Chris getting 2 jobs.

e. If all eight jobs are assigned to the children with one child per job, there are 8! ways to assign the jobs, giving us a total of 8! = 40,320 ways to assign all eight jobs to the children.