II. Examples and Discussion . Read and understand the problem given below. We are about to begin solving problems involving permutation...As we discussed earlier, there are several kinds/types of permutation. All of these can be found in the problem below. 1. OCNHS will conduct a beauty pageant. Search for Ms. OCNHS. For this year 10 students join on the said event. In how many ways can 3'd runner up, 2nd runner up, 1st runner up, and the title holder be selected? Given: n= 10 1=4 Formula: nPr = n! / (n-r)! , ner Solution: 10P4 = 101/ (10-4)! Substitution = 10! / 6! Simplify = 10x9x8x7x6x5x4x3x2x-1 6x5x4x3x2x1 = 10x9x8x7 10 P4 = 5. 040 possible ways5. How many different sequences of five letters can be created from the first 7 letters of the alphabet if no letters are the same. 6. In how many different ways can you arrange 8 figurines on a shelf? 7. There are 4 different Math books and 5 different Science books. In how many ways can the books be arranged on a shelf if a. there are no restrictions? b. books of the same subject must be placed together? c. If they must be placed alternately? 8. Five couples want to have their pictures taken. In how many ways can they arrange themselves in a row if a. couples must stay together? b. they may stand anywhere? 9. There are 12 people in a dinner gathering. In how many ways can the host (one of the 12 ) arrange his guests around a dining table if a. they can sit on any of the chairs? b. 3 people insist on sitting beside each other? c. 2 people refuse to sit beside each other? 10. A teacher drew a number line on the board and named some points on it. The teacher then asked the class to list all the rays in the figure. A student answered 30 rays in all and the teacher said it was correct. How many points were named in the figure