Multi-case Combinations

Question 1

A pirate ship has 6 different flags. If they are always displaying at least 2 flags, how many different arrangements of flags are possible?

Answer 1

at least 2 = 2 flags + 3 flags + 4 flags + 5 flags + 6 flags

= 6x5 + 6x5x4 + 6x5x4x3 + 6x5x4x3x2 + 6x5x4x3x2x1 = 1950

Question 2

If you must make a word from the letters e, r, v and p and at most you can use 3 letters, how many words are possible?

Answer 2

at most 3 = 1 letter word + 2 letter word + 3 letter word = 4 + 4x3 + 4x3x2 = 40 possible words

Question 3

If you are choosing ice cream toppings from 8 different toppings, how many options are possible if you can choose 4 or less toppings?

Answer 3

4 or less = 1 topping + 2 toppings + 3 toppings + 4 toppings = 8C1 + 8C2 + 8C3 + 8C4 = 162 possible options for your ice cream