advertisement

M166 Ch 6 – Permutation and Combination (6.3, 6.4) TAMU – Spring 2014 Calculator Functions: 1. Factorial : MATH → scroll to PRB → scroll to 4 : ! → ENTER Example: Find 5! . Enter 5 → MATH → scroll to PRB → scroll to 4 : ! → ENTER 2. Permutation : nPr Enter n → MATH → scroll to PRB → scroll to 2 : nPr → Enter r → ENTER Example: Find P(5 , 2) . Here, n = 5 and r = 2. Enter 5 → MATH → scroll to PRB → scroll to 2 : nPr → Enter 2 → ENTER 3. Combination : nCr Enter n → MATH → scroll to PRB → scroll to 3 : nCr → Enter r → ENTER Example: Find C(5 , 2) . Here, n = 5 and r = 2. Enter 5 → MATH → scroll to PRB → scroll to 3 : nCr → Enter 2 → ENTER 4. Binomial Trials: a) binompdf – Exactly k successes 2nd VARS → scroll down to A : binompdf( → Enter n → Press the Comma key → Enter p → Press the Comma key → Enter k → ENTER where n : Total number of trials ; p : probability of a success ; k : number of successes b) binomcdf – at most k successes 2nd VARS → scroll down to B : binomcdf( → Enter n → Press the Comma key → Enter p → Press the Comma key → Enter k → ENTER Note : “binomcdf” function is also used to calculate “at least” k successes. We'll discuss in class how that's done. 1 M166 Ch 6 – Permutation and Combination (6.3, 6.4) TAMU – Spring 2014 1. A card is picked from a standard deck of 52 cards and then a 6-sided die is rolled. How many possible outcomes are there? 2. Kitty has 3 dolls, 4 doll- dresses, and 5 doll - shoes. How many different ways can a doll be dressed? 3. In how many different ways can the digits in the set S = {1, 2, 3} be arranged? 4. How many ways can 10 kids be lined up to form a queue? 5. At an award ceremony, 5 couples are to be called one at a time to receive an award. In how many ways can this be done if a) men and women must alternate? b) Couples are called together ? 2 M166 Ch 6 – Permutation and Combination (6.3, 6.4) TAMU – Spring 2014 6. A password can be formed with 4 letters followed by 5 digits. How many different passwords are possible if a) repetition of digits and/or numbers is allowed? b) repetition of letters is not allowed? c) repetition of digits is not allowed? d) the first digit must be non-zero ? 7. Ted loves traveling. He wants to visit 7 cities in Great Britain, 5 in France, 3 in Germany and 4 in India. How many ways can his itinerary be made out? 3 M166 Ch 6 – Permutation and Combination (6.3, 6.4) TAMU – Spring 2014 8. 10 friends decide to take a road-trip and rent a mini van. How many seating arrangements are possible if only 4 of them know how to drive? 9. Linda has 40 books, of which 17 are fiction, 6 are self – help, 13 are textbooks, and 4 are cook-books. How many ways can she arrange all the books on a shelf if a) there are no restrictions on the arrangement ? b) books of the same category must be placed together ? c) there's room for only 25 books ? 4 M166 Ch 6 – Permutation and Combination (6.3, 6.4) TAMU – Spring 2014 10. How many different (distinguishable) ways can we arrange the letters of the word MISSISSIPPI. 11. If there are 3 red, 5 green, and 4 blue balls, how many ways can the balls be arranged, given the balls of same color are exactly alike? 12. Out of a total of 10 people, a committee needs to be formed with a President, a Vice-President, a Secretary, and 3 members. How many ways can the selection be made? 5 M166 Ch 6 – Permutation and Combination (6.3, 6.4) TAMU – Spring 2014 13. An exam consists of 5 true/false questions followed by 3 multiple choice questions each with 4 answers. How many ways can a student answer all the questions if a) he/she has to answer all the questions? b) he/she is allowed to leave the questions blank? 14. A committee of 15 people consists of 8 men and 7 women. Find ( i ) the number if ways of choosing a subcommittee of 5 people consisting of a) any 5 committee members b) all men? c) exactly 3 men? d) at least ? e) at most 3 men ? 6 M166 Ch 6 – Permutation and Combination (6.3, 6.4) TAMU – Spring 2014 15. A pen holder holds 5 green, and 3 blue pens. In how many ways can you select a) 4 pens ? b) 4 pens, with at least 2 blue pens ? c) 4 pens, with exactly 1 blue ? d) 4 pens, with no blue pens ? e) 4 pens, such that exactly 3 are of the same color ? 7 M166 Ch 6 – Permutation and Combination (6.3, 6.4) TAMU – Spring 2014 16. An unfair coin is flipped 100 times in succession. The probability of getting a heads is 1/3. What is the probability of getting a) exactly 40 heads b) At least 40 heads c) At most 40 heads d) More than 40 but less than 60 heads e) exactly 40 tails 17. Your quiz has 10 multiple-choice questions over the material that has not been covered in class. You guess on each question. What is the probability of you getting exactly 7 questions correct? 8