What is the number of ways in which 3holiday travel tickets to be given to 10 employees of an organization, if each employee is eligible for any one or more of the tickets? (b) 120 (a) 60 (d) 1000 (c) 5000

Explanation

There can be three cases.

`Case 1:` When all three tickets are given to one employee.

Number of ways in this case ` = C(10,1) = 10`

`Case 2:` When two of the tickets are given to same employee and third ticket is given to another employee.

Number of ways in this case ` = C(10,2)C(3,2)2! = 45*3*2 = 270`

`Case 3:` When all of the tickets are given to different employees.

Number of ways in this case ` = C(10,3)3! = 120*6 = 720`

So, total number of ways in all three cases ` = 10+270+720 = 1000`