gateacademy testseries

Question

In how many ways can seven different jobs be assigned to four different employees so that each employee is assigned at least one job and the most difficult job is assigned to the best employee?

Answer 1

Every job is distinct and person is also distinct

let jobs are =  j1,j2,j3,j4,j5,j6,j7 (j1 is most difficult and j7 is easy)

person are = p1,p2,p3,p4 (p1 is best , p4 is least best)

as given j1 is handled by p1 only so we have only 5 jobs left(j2 to j7)

at lease one job done by each person will be like

total ways – every process not done by (p2 to p4, p1 is handling j1)

total ways = 4^6 ( each job(j2 to j7) has 4 possibility = 4096

every process not done by (p2 to p4) = all the jobs done by p1 = 1^6 = 1

total ways = 4096 – 1 = 4095