Combinations + Permutations

Question 1

Combinations

Answer 1

when order doesn’t matter

Question 2

Combinations: # of people in the group + total number of groups

Answer 2

They’ll ask you to figure out the different number of k-person groups if you have 56 different group possibilities and total group of people = 8

= (8)C(K) –> this is when you can do backsolving and use the different numbers given in the answer choices to substitute for k and see what gives you 56. since 7*8 = 56, you can assume that the K number you’re looking for will need to cancel out all numbers but 8 and 7.

Question 3

Combinations + Circles/Triangles

Answer 3

If given a circle, and you’re trying to figure out the number of triangles that can be made from X points on the circle, you should use combinations since a triangle is made up of 3 distinct points and they can’t be repeated and order doesn’t matter.

Ex. 7 points on a circle. what’s the # of triangles that can be formed?
(7)C(3) –> 35

Question 4

Fundamental Counting Principle + Combinations

Answer 4

You might need to use Combinations within a fundamental counting principal question when it asks to select more than option for a given category.

Ex. Select 1 main dish, 2 different side dishes and 1 dessert.
-the two different side dishes gives a clue that you’ll need to use combinations to solve this category and not FCP since it’s not a 1:1

If there are 3 main dishes, 4 side dishes and 2 desserts, you’d find the answer by doing:

3 (mains)*6 (sides) *2 (desserts)

6 is found via (4)C(2)