In most likelihood, you will only get one or two combinations/permutations questions per test. Typically, the questions are quite challenging. Knowing the standard formulas won’t be enough; you’ll also have to use logic, and a fair amount of grit. Below is a question that will really force you to think, and rely on that grit. If you can get this question right in under 2 minutes, without a bead of sweat falling from your brow, then you are most likely ready for anything the GRE will throw you test day, combinations/permutations-wise.
Answer and explanation coming soon. Until then, let’s see who can get it. Good luck! 🙂
A space program is recruiting a team of astronauts to journey to Mars aboard a four-person shuttle. If the number of possible teams is less than 100 but greater than 10, then what is the possible number of astronauts who did not make the space team? Indicate all such numbers.
Answer and Explanation:
Two things to pay attention to here:
1) There will be four astronauts on the shuttle
2) We do not want the possible number the program is choosing from; we want the possible number of astronauts who do not make the team.
Let’s call x the number we are choosing from. Using the combinations formula, since we are choosing for a team and the order does not matter, we get:
10 < x!/(x-4)!(4!) < 100
Finding the values for ‘x’, we get a range of 6 to 8. To illustrate:
6!/(6-4)!4! = 15
8!/(8-4)!4! = 70
We know x = 7 will fall inside the range. Therefore, x can equal 6, 7, or 8. Now here’s where we want to pay attention to 2). The number who will not make it will be x – 4. Which yields, 2, 3, or 4 (Answers: F, G, H).