20 people out of 500 people are gonna be chosen as officials. They need :

• one president
• one vice-president
• three secretaries
• and fifteen regular committee members.

1. Determine the total number of different officials that can be formed in this way. (Official A & B are considered the same if they have the same members and the role of every member in A is the same as their role in B. In particular, two of the officials with the same members are considered different if the member have different roles.)
2. Each of the 500 people is assigned a unique positive integer from 1 to 500. If 25 of the officials have been chosen randomly such that no two Official share any members, what is the probability that the first 5 officials consist of the people with the numbers 1 through 100? Assume that all of outcomes are equally likely.