Probability with Combinatorics

Question

Beth and Shanya each purchase one raffle ticket. If a total of eleven raffle tickets are sold and two winners will be selected, what is the probability that both Ben and Shanya win?

Answer 1

The first ticket drawn has a 2/11 chance of being either Beth or Shanya.  If both of them are going to win, its assumed that this first drawing will be one of them.  After that, there are 10 raffle tickets left, and one of them left to win, so the odds of the second person winning would be 1/10.  We multiply 2/11 * 1/10 = 2/110.  You can reduce this further to 1/55.  So the odds of both of them winning are 1 in 55.