A class is choosing a president and a vice president.There are three students running for president: Ann,  Maria,  and Linda.There are three students running for vice president: Bob,  Jim,  and John.The tree diagram below shows the possible outcomes. Use the diagram to answer the questions.PresidentAnnMariaLindaVicePresidentBobJimJohnBobJimJohnBobJimJohnOutcome, AnnBob, AnnJim, AnnJohn, MariaBob, MariaJim, MariaJohn, LindaBob, LindaJim, LindaJohn

1.1. The Westminster Math Club has 4 members: Ayanna, Beatrice, Charles,and Dante. How many different ways are there to choose a President and VicePresident for the club? List all possibilities. (For example, one possibilitywould be to have Ayanna as President and Dante as Vice President.)1.2. Make a table for the number of ways to choose a President and Vice-President for the club if the club has between 2 and 5 members. Note thatyour answer from Problem 1.1 will be one of the entries in this table.1.3. Plot your results from the table in Problem 1.2 on a graph, where thex-coordinate represents the number of members of the Westminster MathClub, and the y-coordinate represents the number of ways to choose thePresident and Vice-President. Be sure to label your points and horizontaland vertical axes.1.4. Make a table of points satisfying the equation y = x2 for x = 2, 3, 4,and 5.

The bowling team at Lincoln High School must choose a president, vice president, and secretary. If the team has 12 members, how many ways could the officers be chosen?

There are 7 students in a classroom Alice, Mike, Ben, Lisa, Paul, Mary, and Bob seated in one row. Mike is between Alice and Lisa but not adjacent to both of them and Alice is on the left side of Mike. Mary is on the left of Alice and Paul is on the right of Ben. Lisa is between Ben and Paul and Ben is on the left side of Lisa. Who is at the fifth and sixth position from the right end of the row?Ben and MikeMike and BobBob and AliceAlice and Mary

Direction : Five students Ram, Rakesh, Rahim, Pawan and Vivek belongs to five different houses A, B, C, D and E but not in order. They all five take participation in 100 m race event. Pawan does not belong to house B, C or D and no one finish race before him. The student from house E finished at last. The runner-up of the race belongs to house B. Rahim finished race just before Vivek. Three persons finished the race before Rahim. Rakesh does not belong to house B or D. Which of the following pair is correct?Vivek - 4thB - 2ndRam - DC - 5th

Three students (S) and six faculty members (F) are on a panel discussing a newcollege policy.(a) In how many different ways can the nine participants be lined up at a table in thefront of the auditorium?(b) How many lineups are possible, considering only the labels S and F?(c) For each of the nine participants, you are to decide whether the participant did agood job or a poor job stating his or her opinion of the new policy; that is, give each of thenine participants a grade of G or P. How many different ”scorecards” are possible?