How would i work this out?

Question

A company has 10 members on its board of directors. In how many ways can it elect a president, vice-president, secretary, and treasurer?

1) 210

2) 320

3) 5,040

4) 30,240

Answer 1

Ok, so we have to think about the problem and what is going on.  Since the people being selected will hold specific positions, the order will be important.  Because if the first person chosen is President, that same person being chosen 2nd would be Vice President, and therefore a completely different way of electing the directors.

 

Since order is important, we are working with a Permutation.

 

Since we are choosing 4 people out of the total 10, it is ₁₀P₄

 

That will give us 5040 different ways to elect our Board of Directors.