3.Fifteen math majors are in the department lounge causing trouble and bullyingthe Computer Science majors. The chair of the department, The Billster, has two tasks tobe completed. The first is to fill Billster's car with gas which he figures will require threemath majors to complete. The second is to check the spelling on the department welcomesign which will require four math majors to complete. How many ways can these tasks beassigned to the fifteen math majors? How many ways can they be assigned if each task alsorequires that one person be put in charge?a student can only do one task at most and cannot be assigned to two tasks at the same time.For example, a student would not be assigned to proof read and service a car.

Given Information:15 math majors are there in the department lounge.Billster assign 3 of them to service a car and 4 of them to proof read.No student assigned to both tasks.To find:The number of ways the task be assigned to 15 math majors.The number of ways the task be assigned to 15 math majors incase one person as in charge.Concept used:The number of objects have been chosen from number of objects inThe task of proof read and car service are independent.The total number of ways to assign the student with both the tasks is the sum of the ways to assign them in both the tasks.Billster assign 3 math majors from 15 math majors to the task of car service. The number of ways to assign the car service is that .As 3 students assigned to the car sevice, the students 12 of 15 math major only assigned to the proof read task.Billster assign 4 student from 12 math majors to the task as proof read.The number of ways to assign the proof read is .Both the task can be done independently and simultaneously.So, the total number of ways is the product of the number of ways the person can choose in each way.The total number of ways to assign the person on both the task without incharge is First, Billster assign 3 from 15 to the task of car service.One person is as incharge. So, there are 15 choices as become to assign incharge.From the rest 14 choices, choose 2 person to service the car.The total number of ways to assign the student to service the car is as both the choice of incharge and task worker as independent.Now, 3 persons are assigned to the car service. So, only for 12 persons can able to assign proof reading task.Among 12 persons, there are 12 ways to assign 1 person as incharge.From the rest 11 persons, we have to assign 3 persons to the task of proof reading.The total number of ways to assign the student to proof reading task is .Both the task can be done independently and simultaneously.So, the total number of ways is the product of the number of ways the person can choose in each way.The total number of ways to assign the person on both the task with incharge is .The total number of ways to assign the person on both the task without incharge is ways.The total number of ways to assign the person on both the task with incharge is ways.