Final answer:
The board can elect a president in 823,543 different ways.
Step-by-step explanation:
The board can elect a president in 7 different ways. Each member of the board can be elected as the president, so there are 7 choices for the first member, 7 choices for the second member, and so on, until the seventh member. To find the total number of different ways, we multiply the number of choices for each member: 7 x 7 x 7 x 7 x 7 x 7 x 7 = 7^7 = 823,543.
The question is asking about the number of different ways to elect a president from a board of directors consisting of 7 members. Essentially, this is a problem of permutations where order does matter, but we are only interested in the first position, the president. Since there is only one position to fill, the number of ways to elect a president is the same as the number of members on the board. Therefore, there are exactly 7 different ways to elect a president from a board of 7 members.