Question 349036: An employer has 8 different tasks that he wants completed by his four employees. Each of the tasks is to be done by one employee. The employer wants to distribute the tasks so that each employee gets assigned at least one task but not more than three tasks. How many different ways are there to assign the 8 tasks?
I attempted to draw a tree diagram to get the solution to this problem but I believe that led me in the wrong direction. How do i solve this using the correct formula?
Answer by sudhanshu_kmr(1152)   (Show Source):
You can put this solution on YOUR website! There are 8 tasks and 4 employee, according to question each one get at least 1 or almost 3 task
so possible conditions are (2, 2 , 2, 2), (3,1,1,3)and (1,3,2,2)
case 1: when each will get 2 tasks...
no. of ways = 8C2 * 6C2 * 4C2 * 2C2 = 28*15* 6*1 = 2520
case 2: when two have 3 task and two have 1 task
it can be arrange in 4!/ {2!*2!) = 6 ways
like 1133,3311,......
no. of ways = 6 * [ 8C3 * 5C3 * 2C1 * 1C1 ]= 6 * 56*10 *2*1 = 6720
case 3: when one have 3, one have 1 and two have 2 tasks..
it can be arrange in 4!/2! = 12 ways
no. of ways = 12 * [ 8C3 * 5C2 * 3C2 * 1C1 ] = 12 * 56 * 10 * 3 *1 =20160
total no. of ways = 2520 + 6720 + 20160 = 29400
|
|
|
