Question

1. (5) 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

ANSWER:

• We recognize with the purpose of he intends to capture at least 2 small monsters of every category, i.e 2 small fire monsters, 2 small water monsters and 2 small grass monsters.
• He as well intends to capture by the side of smallest amount 3 small fire monsters.

therefore,

• He have to capture at least 3 small fire monsters, 2 small water monsters and 2 small grass monsters.
• therefore, 7 of the small monsters are permanent.
• The rest 13 be able to be several of fire, water or grass small monsters.
• This is a classic case of the stars and bars trouble, the explanation to which is (n+k-1)Cn.
• now n is 13 and k is 3. So, the number of combinations is

(13+3-1)C13 = 15C13

= 105.