Concept:The tickets are considered distinct, and each employee may receive any number of them.
We count selections by dividing into cases based on how many employees get tickets.
Explanation:Step 1: All three tickets to the same employee.
Choose the employee:
10C1=10 ways.
Step 2: Two tickets to one employee and one ticket to another.
First, choose two distinct employees:
10C2=45 ways.
From the 3 tickets, choose the two that go to the first employee:
3C2=3 ways.
The remaining ticket automatically goes to the second employee.
Multiply by
2! because the two chosen employees can be swapped (who gets two tickets and who gets one):
45×3×2=270 ways.
Step 3: All three tickets to three different employees.
Choose 3 employees:
10C3=120 ways.
Distribute the 3 distinct tickets among them in
3!=6 ways.
Total:
120×6=720 ways.
Add the cases:
10+270+720=1000 total ways.
Answer:1000