Objective: Solve problems involving different permutations and permutations with some extra conditions. Solve the following problems. Show your complete solution in another sheet of paper. 1. In how many ways can 4 girls and 4 boys be seated in a row containing eight seats, a. if they may seat anywhere? b. if the boys and girls must alternate? 2. A math teacher wants to keep books of the same book together on his shelf. If he has 12 spaces for 5 Algebra, 4 Geometry, and 3 Trigonometry books, in how many ways can they be placed on a shelf? 3. In how many ways can 6 people be seated around a table? 4. In how many ways can 6 people be seated around a table if two people insist on sitting next to each other? 5. In how many ways can the letter of the word HONESTY be arranged? 6. Find the number of permutations of the number 1, 2, 3, and 4 taken two at a time. 7. In how many ways can 11 different colored beads be arranged on a bracelet? 8. In how many ways can 10 books, 2 of which are Math, 5 are Chemistry, 3 English, be arranged on a shelf if they are to occupy just one row? 9. Suppose an identical twin, identical triplets and two other children pose for a photograph. How many photographs will be different? 10. A spinner is to be divided into four equal parts. In how many different ways can you arrange four symbols in the spinner? 1 1. If 4 persons enter a bus in which there are 10 vacant seats, how many ways are there for the 4 to be seated? 12. Suppose 7 students are staying in a hall in a hostel and they are allotted 7 beds. Among them, Joey does not want a bed next to Troy because Troy snores. Then, in how many ways can you allot the beds? 13. In how many ways can animal trainer arrange 5 lions and 4 tigers in a row so that no two lions are together? 14. There are 4 books on fairy tales, 5 novels and 3 plays. In how many ways can you arrange these so that books on fairy tales are together, novels are together and plays are together and, in the order, books on fairy tales, novels and plays? 15. In how many ways can 7 students be seated in a: a. row b. round table, if two particular students must not be seated next to each other