Step by step
The question
Question: A club of 10 people picks a president and a vice president at random.
What is the probability that Ann is president and Ben is vice president?
The probability is the number of ways we want, over all the ways.
P stands for probability.
1 Order: yes or no
Does order matter?
Yes.
Ann president and Ben vice is not Ben president and Ann vice.
So we count permutations.
2 Count all the ways
10 P 2: 10 choices for the first place, then 9 for the second.
10 times 9 is 90 ways.
3 Count the ways we want
Only one way: Ann president and Ben vice.
So 1 way.
4 Write the fraction
1 way we want, out of 90.
Careful!
Not 10 C 2: that counts groups.
Here the places are different, so order matters.
5 Check
Let's check another way: one place at a time.
Ann president: 1 out of 10.
Then Ben: 1 out of the 9 left.
Multiplied, that is 1/90.
The same.
So the answer is right!
Let's look back.
First: order: yes or no.
Then: count all the ways.
Then: count the ways we want.
Then: write the fraction.
Last: check.