I. Knowledge: A. Write down the formula that is best suited for the situation 1. 2. 3. 4. 5. 6. 7. Fundamental counting principle Permutation of n objects taken r at a time Permutation of n objects taken n at a time Permutation with identical objects Permutation of n distinct objects arranged in a circle Permutation of n different objects around a ring Combination of n different objects taken r at a time B. Answer the following questions 1. It is the field of mathematics that deals with chance. _____ 2. It is an activity in which the results cannot be predicted with certainty. _____ 3. It is the repetition of an experiment. _____ 4. It is the result of an experiment. _____ 5. It is any collection of outcomes. _____ 6. It is an event with only one possible outcome. _____ 7. It is the set of all possible outcomes of an experiment. _____ 8. It is the measure of likelihood that an event will happen. _____ 9. It is the set of all outcomes not in the event. _____ 10. These are events that cannot happen at the same time. _____ II. Process: Answer each given situation below. Show complete computations, then box all final answers. Express all probabilities in fraction form. 1. A restaurant has 5 appetizers, 8 beverages, 9 entrees and 6 desserts on the menu. How many possible full meal sets can the restaurant serve? 2. How many 5-digit telephone numbers can be constructed using the digits 0 to 9, if each number starts with 67 and no digit appears more than once? 3. Find the number of permutations of the letters of the word ALLAHABAD. 4. In how many ways can five couples seat themselves around a circular table if: a. Spouses sit opposite each other b. Men and women are seated alternately 5. Four different math books, six different physics books and two different chemistry books are placed on a shelf. What is the number of possible arrangements if: a. The textbooks from each subject must be grouped together b. Only the math textbooks need to be grouped together 6. Eight cars enter a race. The three fasted cars will be given first, second, and third places. How many arrangements of first, second, and third places are possible? 7. There are 18 students in a classroom. How many different 11-person students can be chosen to play on a football team? 8. Mike is playing cards with his sister when he draws a card from a pack of 35 cards numbered from 1 to 35. What is the probability of drawing a number that is divisible by 5? 9. A bag contains fifteen red balls, twelve pink balls, and eight yellow balls. You pick one without looking. What is the probability that the balls will be either yellow OR pink? 10. You think of a number from the first twenty positive integers. What is the probability that the integer chosen will be divisible by 4? 11. A basket contains 5 apples and 7 peaches. You randomly select one piece of fruit and eat it. Then you randomly select another piece of fruit. What is the probability that the first piece of fruit is an apple and the second piece is a peach? 12. There are eight shirts in your closet, 4 blue and 4 green. You randomly select one to wear on Monday and then a different one on Tuesday. What is the probability that you wear blue shirts on both days? 13. A box contains 5 red marbles and 7 green marbles. Find the probability of drawing 2 red marbles: a. With replacement b. Without replacement 14. From a standard deck of cards, what is the probability of choosing: a. a red and then a club with replacement? b. a 3, then a 7, then a face card without replacement? c. a diamond, then a heart, then a black card without replacement? d. a number card and then a face card with replacement?
