"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.
Game Station 3: JUMBLE- The team that completes the Jumble first gets 5 points
A. How many possible combinations are there for the letters in the three
circles for the second clue word in this puzzle - ZIGOM?
B. How many possible combinations are there for the letters in the three
circles for the third clue word in this puzzle - CURICS?
Game Station 4: Spinner of 4 equal parts: Red, Purple, Green and Orange - Rules: If the arrow lands in the red quadrant, "Team Y" gets 7 points. If it lands in the other quadrants, both teams lose 1 point.
A. "Team Y" spins 5 times. How many of the possible outcomes could have landed in Red exactly 3 times and on purple exactly 2 times? c
B. "Team Z" spins 4 times. How many of the possible outcomes could have landed in Red exactly 3 times?
C. "Team Y" spins 5 times. How many of the possible outcomes could have landed in Red at least once?
Station 5: PRIZES The 150 supporters of the two teams were surveyed about the prize for each member of the winning team. 30 selected the phone, 50 selected the gaming console, 40 selected the laptop, 20 selected the phone and the gaming console, 25 selected the laptop and the gaming console, 15 selected the phone and the laptop, 5 selected all three
A. Create a Venn diagram for the situation above.
Notation: P - phone set, G - gaming console set, L - laptop set
B. Use the Venn diagram to determine the number of supporters that:
Selected only one award :______ Selected exactly two awards : _____ Did not complete the survey:_____
C. Use the Venn diagram above to determine the number of supporters in each subset:
: _______ ∩ ∩ : _______ ∪ ∪ : _______ ∩
: _______( ∪ ) ∩ : _______ ∪ ( )’: _______ ∪ ∪
Station 6: High-Fives - The competition is over! The 3 members of "Team Y" high-five each other. The 4 members of "Team Z" high-five each other. The supporters high-five each other.
A. In how many ways can the members of "Team Y" high-five each other only once?
B. In how many ways can the members of "Team Z" high-five each other only once?
C. In how many ways can the 150 supporters high-five each other only once?
