A consulting firm has received $2$ Super Bowl playoff tickets from one of its clients. To be fair, the firm is randomly selecting two different employee names to "win" the tickets. There are $6$ secretaries$,5$ consultants, and $4$ partners in the firm. Which of the following statements is true?

Incorrect Response

The probability of two secretaries winning is the same as the probability of a secretary winning on the second draw given that a consultant won on the first draw.

The probability of a secretary and a consultant winning is the same as the probability of a secretary and secretary winning.

The probability of a secretary winning on the second draw given that a consultant won on the first draw is the same as the probability of a consultant winning on the second draw given that a secretary won on the first draw.

The probability that both tickets will be won by partners is the same as the probability that a consultant and secretary will win.

Correct Answer

None of the above are true.