Question

If a small monster collector has 20 small monster containment devices; intends to use all of those devices; has access to non-unique Water, Fire and Grass type small monsters; intends to capture at least two small monsters of each type; and intends to capture at least three Fire-type small monsters - how many different combinations of small monster types can that collector capture?

Answer 1

The collector can capture nine different types of combinations of monster types.

Explanation:

• There are twenty small monster containment devices. The collector has access only to non-unique types. They are water, fire and grass types of small monsters.
• The collector will capture at least two of the small monsters of each type. So he will capture two types of water, two types of fire and two types of grass. After that, he will capture three different types of fire monsters.
• So he will capture nine different types of monsters.

Answer 2

In mathematics, a combination refers to a method of selecting items from a sample where the order in which the elements of the sample are arranged does not matter.

What is the formula for Combination?

C = (n, r) = $\frac{n!}{(r!(n-r)!)}$

where n is the number of objects and

r the sample.

There are 3 categories of monsters:

• non-unique Water
• Fire and
• Grass-type small monsters;

He intends to catch at least two of each type. This is represented mathematically as:

C(3, 2) = 3!/(2!(3-2)!)

= 3!/2! x1!

= 3

He also intends to capture at least three fire-type monsters.

This is represented as:

C (3, 1) = 3!/(1!(3-1)!)

= 3!/1!x2!

= 3

Hence the different number of combinations are:

3+3 = 6

Learn more about Combinations at:

https://brainly.com/question/11732255