sukhman wrote:A student committee on academic integrity has 90 ways to select a president and vice-president from a groupof candidates. The same person cannot be both president and vice-president. How many students are in the group? Answer 10
Slightly different approach, same result.
Let's let x = the number of students.
Take the task and break it into stages.
Stage 1: Select a president
There are x students to choose from, so we can complete stage 1 in
x ways
Stage 2: Select a vice-president
There are x-1 students remaining, so we can complete stage 2 in
x-1 ways
By the Fundamental Counting Principle (FCP) we can complete both stages
(x)(x-1) ways
Since we are told that there are 90 ways to select a president and vice-president, we can conclude that:
(x)(x-1) = 90
At this point, there would be answer choices, so we could just start plugging in values for x, to get x =
10
Cheers,
Brent
Aside: For more information about the FCP, watch our free video:
https://www.gmatprepnow.com/module/gmat-counting?id=775
