Problem 6. (10 pla.) Cardinality, Counting Techniques (a) (2 pts.) Fill in the provided Venn diagram if n(A) = 10,"(B) = 13, =(A UB) - 20. 10 (b) (6 pta.} You are building a team of three Pokemon to battle your rival. . You want the first Pokemon to be your Umbreon. . You want the second Pokemon to be either normal or ice type, and you have 3 normal Pokemon or 3 ice Pokemon to choose from. . You want the final Pokemon to be either psychic, grass, or bug type. You have 3 psychic Pokemon, 2 grass Pokemon, and 4 bug Pokemon. Fill out the decision algorithm {3 pta. } and determine how many outcomes are possible (3 pts.). Step 1: 1" Pokemon Step 2 2" Pokemon Step 3: 3"d Pokemon outcome(s) Alt 1: Normal Alt 1: Psychic 3 outcome(s) 3 outcome(s) All, 2: Ice Alt 2: Grass 13 outcome(s) 2 outcome(s) Alt 3: Bug _outcome(s) How many outcomes (Pokemon teams) are possible? 54 Pokemon teams (c) (2 pts.) Uh oh! After selecting your team, you dropped your Pokemon. You had three Pokebalis in your hand and you pick them back up. How many possible orders are there to pick up three balls