A real-life question regarding probabilities

I have a real-life math question regarding probabilities. My daughter works for a large bank and is in charge of the committee that is planning a holiday event for all the employees. This event will include a raffle.

Here are the details:

Number of attendees: 123

Number of prizes: 26

Number of tickets: 5 for each employee = 123 x 5 = 615 tickets

The individual prizes will be displayed on tables next to a container that will hold the tickets. Each attendee may place one or more of their allotted five tickets into any prize container. Obviously, the more tickets one places in a single prize container, the greater the chances of winning that prize.

When the actual drawing occurs, a committee member will randomly select a single ticket from the ticket container for that particular prize. The winner will be announced and the next drawing will proceed. Each of the 26 drawings will occur sequentially until the last prize is awarded.

There is some dissension within the committee as to whether a single attendee will be allowed to win more than one prize. To help with this decision, I would like to calculate the chances of any one individual's ticket(s) being drawn more than once.

Based on the numbers above, can someone help me determine the probability of any one single person winning more than one prize?