Question

A group of 10 people is choosing a chairperson and vice-chairperson. They put all 10 people's names into a hat. The first name drawn becomes chair. The second name drawn becomes vice-chair. How many possible combinations of chair and vice-chair are there?

a.19
b.90
c.100
d.10! (10 factorial)

Answer 1

B.90

Explanation:

As there are 10 people and choosing chairperson occurs first as an independent event

=> The number of possible chairperson is 10.

After the chairperson is chosen, the number of names left in the hat is 9

=> There are 9 possible vice-chair.

However, the names left in the hat depends on which name is elected as chairperson

=> Choosing vice-chair is a an event dependent on the first event.

=> The number of possible combinations of chair and vice chair would be:

9x10 = 90