We are told that 15 people entered a giveaway for 3 movie tickets. We are asked to find the probability that Jodi, Dan, and Pilar all won the tickets. To do that, we will first find the number of possible outcomes of the giveaway. Since the order of the winners does not matter, we will use combinations.
Combinations
The number of n distinct objects taken r at a time is denoted _nC_r and can be calculated using the following formula.
_nC_r=n!/( n- r)! r!
There are 15 people participating in the giveaway and 3 of them will win the tickets. Therefore, we can substitute n= 15 and r= 3 into the formula to find the possible numbers of outcomes of the giveaway.
We found that there are 455 possible combinations of the winners of the giveaway. Therefore, the probability that Jodi, Dan, and Pilar win the tickets, which is only one of the combinations, is 1 divided by the number of possible combinations, 455.
Probability=1/455
