Question

a. What are the maximal and minimal elements, if any, of the set (N+,|)? Is there a minimum or maximum element? (N+={1,2,3,4,...}).

b. There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. We can have three scoops. How many variations will there be?

Answer 1

a.

N = {1, 2, 3,...}

The minimal element of this set is 1. But since this is unbounded above so maxiy element don't exist.

b.

If all 3 scoops have the same flavour the there are 5C₁ = 5 possibilities.(as there are five flavors of ice cream)

If 2 scoops with the same flavour and 1 with different flavor of ice cream then there are 2× 5C₂ = 20 = 5×4 possibilities.( For if two scoop is filled with one type of ice cream then third schoop can be filled by 4 flavors, there are 5 ways in which two scoops can be filled by same type of ice cream as there are 5 types of ice cream so 5×4) or (first find how many ways you can choose 2 flavors: 5C₂. Then remember that there are 2 ways to have 3 scoops of 2 flavors, such as with chocolate and vanilla. 2 scoops vanilla, 1 chocolate, or 2 chocolate, 1 vanilla)

If all 3 scoops have different flavour of ice cream then there are 5C₃ = 10 possibilities.

So there are total 5 + 20 + 10 = 35 variations.