Hi there!

Please find below the solutions to your questions that I came up with:

1. The girls' volleyball team is going to have a practice game, by separating the 12 players into 2 teams of 6 players. What is the probability that Vivian and Veronica will be on the same team?

Ans: 6 players can be arranged out of total 12 people in 12C6 ways = 924 (total number of outcomes). If two players are to be on the same team, then the remaining 4 places on a team should be distributed among 10 other players. This can be done in 10C4 ways = 210 (favorable number of cases). So, the probability that Vivian and Veronica will be on the same team is given by: Probability (Vivian & Veronica on the same team) = 210/924 or 0.22.

2. A small company had 11 female employees and 13 male employees. If 5 employees are to be selected to work on a project and the CEO insists that there be at least 1 employee of each gender working on the project, how many different project teams can be selected?

Ans: If out of 5 people to be selected to work on a project there is at least 1 employee of each gender, then there will be 3 vacant places in a team to be potentially filled up by the remaining 22 people (10 females and 12 males). The number of different project teams that can be selected is given by: 22C3 ways = 1540.

3. The girls' volleyball team is going to have a practice game, by separating the 12 players into 2 teams of 6 players each. If Vivian and Veronica can't be on the same team, how many possibilities are there?

Ans: Probability (Vivian & Veronica NOT on the same team) = 1 - Probability (Vivian & Veronica ON the same team)= =1 - 0.22 = 0.78.

Cheers!