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?

In how many ways can three awards be given to eight students under the following conditions? (See Example 6 in this section.)(a)if each student may receive more than one award

Select the correct answer There are Seven Committee in a college viz., Academic, Alumni, Business, Cultural, Hostel, Placement and Sports. The Academic Committee meets every second day, the Alumni Committee meets every third day, the Business Committee meets every fourth day, the Cultural Committee meets every fifth day and the Hostel Committee meets every sixth day, the Placement Committee meets every Eighth day and the Sports Committee meets every Tenth day. How many times all the Seventh Committee do meets on the same day within days? radio_button_unchecked 12 radio_button_unchecked 9 radio_button_unchecked 6 radio_button_unchecked 3

There are 9 teachers in a group. 3 of them will be chosen to turn out the final paper. How many possible outcomes are there for the team members.

At a certain high school, the Prom Committee is going to choose new members. There are 4 students from the Junior class and 8 students from the Senior class who are willing to be new members. In how many ways can 5 new members be chosen if more than 3 must be from the Senior class?(If necessary, consult a list of formulas.)

A high school has 8 students who want to be class officers. If there are 3 different positions open, how many ways are there for the students to fill them?