A board of directors consisting of eight members is to be chosen from a pool of 28 candidates. The board is to have a chairman, a treasurer, a secretary, and five other members. In how many ways can the board of directors be chosen?

Answer 1

For permutations without repetitions, the formula is n!/((n-r)!), where n is the number of things to choose from, and you choose r of them There is no repetition, and order matters.
Think about it this way. You have 28 candidates total. For the position of chairman, there are 28 possible people. After you select one person for chairmen, there are 27 people left - 27 possible people.
With each position that is filled, you have one less person for the job. At the end, you'll have all 8 positions filled, and 20 people left over.
So then we have 28!/((28-8)!) = 28x27x26x25x24x23x22x21. That should give you your answer.