Question

Here are 9 members on a board of directors. if they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?

Answer 1

Slot A = chairperson position
Slot B = secretary position
Slot C = treasurer position

There are 9 choices for slot A. After picking that person, there are 8 choices for slot B. Then 7 choices for slot C

Multiply those values out: 9*8*7 = 72*7 = 504

There are 504 ways to pick three people from a pool of nine.

Answer: 504

Note: order matters so this is a permutation. You can use the nPr permutation formula with n = 9 and r = 3 to get the same answer