# If they must select a chairperson, first vice chairperson, second vice chair person, and secretary, how many different slates of candidates are possible?There are 11 members on the board of...

If they must select a chairperson, first vice chairperson, second vice chair person, and secretary, how many different slates of candidates are possible?

There are 11 members on the board of directors for the coca cola company.

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### 1 Answer

The number of board members = 11

The number of positions = 4

Let's approach this problem in position by position manner.

First we will fill the number of way to fill the chairperson position. Actually we have 11 ways of doing it, since we have 11 members free.

`n_1 = 11`

For the first vice chairperson position we have only 10 members free **(Since we have already used one as chairperson)**.Therefore we have only 10 ways of filling that position.

`n_2 = 10`

Similarly, for the second vice chairperson we have 9 ways.

`n_3 = 9`

For secretary position we have 8 ways.

`n_4 = 8`

Therefore the total number of ways, N is,

`N = n_1 xx n_2 xx n_3 xx n_4`

`N = 11 xx 10 xx 9 xx 8`

`N = 7920.`

**Therefore there are 7920 ways of selecting persons for the 4 positions.**