(7 POINTS) PAGE 4 OF 13 8) SOLVE THE FOLLOWING PROBLEMS. A) IN HOW MANY WAYS CAN THE LETTERS OF THE WORD "TRACK" BE ARRANGED? B) A STUDENT MUST SELECT AND ANSWER SIX OUT OF TEN QUESTIONS ON AN EXAM. IN HOW MANY WAYS CAN THIS BE DONE? C) A TEACHER DECIDES TO GIVE SIX IDENTICAL PRIZES TO 6 OF THE 20 STUDENTS IN HIS CLASS. IN HOW MANY WAYS CAN THIS BE DONE? D) HOW MANY DISTINCT ARRANGEMENTS CAN BE MADE WITH THE LETTERS IN THE WORD CONNECTION? E) HOW MANY AUTOMOBILE LICENSE PLATES CAN BE MADE IF EACH PLATE CONTAINS 3 DIFFERENT DIGITS FOLLOWED BY 3 DIFFERENT LETTERS? F) IF A BASEBALL TEAM CONSISTS OF 18 PLAYERS, HOW MANY POSSIBLE GROUPS OF 9 MAN TEAMS ARE POSSIBLE? G) HOW MANY DIFFERENT COMMITTEES CAN BE FORMED FROM 4 TEACHERS AND 20 STUDENTS IF THE COMMITTEE IS TO CONSIST OF TWO TEACHERS AND THREE STUDENTS?