Combinations problems
"Team Y" and "Team Z" are competing in a series of games. Answer the following questions:
Game Station 1: Rock, Paper, Scissors - Rules: scissors cut paper, paper covers rock, and rock breaks scissors. Team Y : they have decided that repetition is allowed so they may repeat a previous choice. Team Z: their strategy is to not repeat the previous choice (For example: if in round 1, they play Rock, in round 2 they will only play Paper or Scissors. If in round 2 they play Paper, in round 3, they will play Rock or Scissor...)

A. Create a tree diagram to illustrate the possible plays for each team in 3 matches.



B. In how many possible ways can "Team Y" play in fifteen matches? Repetition allowed.


C. In how many possible ways can "Team Z" play fifteen matches if their strategy is to never repeat only the previous choice?





Game Station 2: Amazing Race- Each team has to match 9 of the 20 banners with the word “Hello” in different languages with the 9 countries that speak that language

A. Determine the number of ways of selecting and matching nine banners with a country.


B. Determine the number of ways of selecting nine banners without having to match them with a country.