Typewritten if possible With solution

Learning Task 1: Solve the following permutation and combination problems. 1. In how many ways can you arrange 5 Mathematics books, 4 Science books, and 3 English books on a shelf such that books of the same subject are kept together? Math English Science EDU 102m-nin 2. In how many ways can 6 students be seated in a row of 6 seats if 2 of the students insist on sitting beside each other? 3. In a gathering, the host makes sure that each guest shakes hands with everyone else. If there are 25 guests, how many handshakes will be done? E Learning Task 2: Answer the following questions. 1. How do you determine if a situation involves combinations? 2. To find the total number of polygons that can be formed from 7 points on a plane with no three of which are collinear. Joy answered: C(7, 3) = 7! 41 31 7.6.5.41 41 3! 7.8.5 3.2-1 = 35 different polygons Is Joy correct? Justify your answer? 3. a. In how many ways can the 12 members of the Board of Directors (BOD) be chosen from 12 parent- nominees and 7 teacher-nominees if there must be 8 parents in the BOD? b. After the 12 members are chosen, in how many ways can they elect among themselves the 7 top positions (president, vice president, and others)