(1) Dante can only invite 8 people to his birthday, but has 13 friends hed like to invite. Eight of his friends are boys and five are girls. If Dante randomly selects 8 people, determine the probability for each scenario.

1. Dante invites exactly 5 boys.

2. Dante randomly invites friends and all are boys.

3. Dante invites an equal number of boys and girls

(2) Connor randomly draws five cards from a 52-card deck. Calculate the probability for each given event.

1. Connor has four Kings

2. Connor has four face cards

3. Connor has four-of-a-kind

4. Connor has at least one face card

(3) Jos has a jar of 43 candy pieces. 17 are red, 11 are blue, 8 are green, and 7 are yellow. He randomly chooses eight pieces of candy. Calculate the probability for each given event.

1. No red pieces are chosen

2. Three pieces are green and two are yellow

3. Five of the pieces are red or blue

4. Six pieces are blue or six pieces are red

5. An equal number of each color are chosen

(4) Local DC residents were asked which area teams they support. 122 support at least one team.

16 support only the Capitols, 16 support the Capitols and Nationals, and 35 support the Capitols and Redskins. 2 support all three teams. 1 support only the Nationals, and 45 support the Nationals and the Redskins. 2 residents do not support any of the teams. Draw Venn diagram and Calculate the probability for each given event.

1. A randomly selected resident supports the Capitols or the Nationals

2. A randomly selected resident supports exactly one team

3. A randomly selected resident supports the Capitols but not the Redskins