Let’s take the problem one person at a time. Have the 25 people reveal their numbers, one after another. We’ll figure the probability that we get 25 different numbers, and then subtract that from 1.0.

When the first person reveals the number, what is the chance that it matches no previous number? Since there *are* no previous numbers, that’s a perfect score of 1.0 When the second person reveals, there are 99 unchosen numbers from which to choose, so the chance is 0.99.

Extend this for all 25 people, and then combine the individual event chances (remember, the *all* must be true — failing to match) to get the chance that none of the 25 numbers match any others.

Does that give you enough of a push?