David and Amelia are graduating in a class of 57 students. If each student is assigned a number from one to 57 at random, what is the probability that David’s number will be one and Amelia’s will be two?
In this case, we’re dealing with two events. Event one is David being selected for number one. There is one chance out of 57 chances that David will be selected as number one. Event number two is that Amelia is chosen for number two. Amelia has one chance of being selected number two out of 56 chances. Why did this value go down from 57 to 56?
It’s because this is a combination of events. Event one happens; David is chosen as number one. After that, there are only 56 remaining numbers that Amelia could be. If someone is already chosen for spot one, Amelia’s chances for being chosen for spot two go up slightly.
But we’re not just interested in their separate probabilities. We want to know the chances that they will both happen. And that means we need to multiply both of these together. One times one is one. 57 times 56 equals 3192.
David and Amelia have one out of 3192 chances of being chosen for numbers one and two.