The number of ways in which 3 holiday tickets can be given to 20 employees of an organization if each employee is eligible for any one or more of the tickets, is

Options

A. 1140
B. 3420
C. 6840
D. 8000

Answer

To solve the problem of distributing 3 holiday tickets among 20 employees, where each employee can receive one or more tickets, we can follow these steps:

### Step 1: Understand the Problem
We need to distribute 3 identical holiday tickets to 20 employees. Each employee can receive any number of tickets, including none.

### Step 2: Determine the Choices for Each Ticket
Since each of the 3 tickets can be given to any of the 20 employees, we need to consider the choices available for each ticket.

- For Ticket 1, there are 20 choices (any of the 20 employees).
- For Ticket 2, there are again 20 choices.
- For Ticket 3, there are also 20 choices.

### Step 3: Calculate the Total Number of Ways
Since the choices for each ticket are independent, we can multiply the number of choices for each ticket together:

\[ \text{Total Ways} = \text{Choices for Ticket 1} \times \text{Choices for Ticket 2} \times \text{Choices for Ticket 3} \]

Substituting the values we found:

\[ \text{Total Ways} = 20 \times 20 \times 20 \]

### Step 4: Perform the Calculation
Now, we calculate \(20 \times 20 \times 20\):

\[ 20 \times 20 = 400 \]
\[ 400 \times 20 = 8000 \]

### Step 5: Conclusion
Therefore, the total number of ways to distribute the 3 holiday tickets among the 20 employees is **8000**.