Pre-Calculus 12 Unit 7 Send-In Assignment On-Line Course SEND - IN ASSIGNMENT UNIT 7 PERMUTATIONS and COMBINATIONS Name: _________________________________________ Teacher:________________________________________ School:_________________________________________ Total ______ = _________% 69 Formulae P n r Version 1 2012 n! n r ! C n r n! r ! n r ! Page 1 of 13 tk 1 n Ck a n k bk Unit 7 Pre-Calculus 12 Unit 7 Send-In Assignment On-Line Course Show all work where possible. 1. BC Place Stadium has 16 gates. In how many ways can you enter the stadium and leave the stadium: a) by a different gate. a) _____________________________ 1 mark b) by any gate. b) _____________________________ 1 mark 2. You bought six numbers at your local hardware store. The numbers are 0, 1, 2, 3, 4, 5. a) How many 4 digit house numbers can you form using these numbers? (note: 0351 is not considered a house number). a) _____________________________ 2 marks b) How many 4 digit house numbers are even? (note: 0351 is not considered a house number). b) _____________________________ 2 marks Version 1 2012 Page 2 of 13 Unit 7 Pre-Calculus 12 3. Unit 7 Send-In Assignment On-Line Course Determine all the possible permutations of all the letters in FACTOR. 3) _____________________________ 1 mark 4. Consider the word AARDVARK. a) Determine all the permutations of all the letters. . a) _____________________________ 2 marks b) determine all the permutations of the letters in which the three A's are together. b) _____________________________ 2 marks 5. How many ways can 4 teddy bears, 3 toy trucks, 5 dolls and 1 toy car be distributed among 13 children if each child is to receive 1 item? a) ____________________________ 2 marks Version 1 2012 Page 3 of 13 Unit 7 Pre-Calculus 12 6. Unit 7 Send-In Assignment On-Line Course How many 4 letter permutations can be formed from the letters in the word FRUCTOSE. *use factorial notation to determine the number of permutation. b) _____________________________ 2 marks 7. In how many ways can a school president, a vice-president, and a secretary be selected from the 21 students comprising the student council? c) _____________________________ 2 marks 8. Seven people attend a movie. There are only 3 seats available in a row. In how many ways can 3 people be seated of the seven? d) _____________________________ 2 marks Version 1 2012 Page 4 of 13 Unit 7 Pre-Calculus 12 9. Unit 7 Send-In Assignment On-Line Course The coach from a soccer team of 15 players must select 11 players for the start of a game. a) Of the 11 players he must select 1 player as the field captain. How many ways can the coach make these selections. a) _____________________________ 2 marks b) Before the game all players line up in a straight line for a team photograph. If 2 players, Michaela and Aleah must be together, then how many different arrangements can be made for the picture? b) _____________________________ 2 marks 10. A true false test has 15 questions. How many answer keys are possible if the answer to 6 of the questions are False and 9 are True? 10) _____________________________ 2 marks Version 1 2012 Page 5 of 13 Unit 7 Pre-Calculus 12 11. Unit 7 Send-In Assignment On-Line Course A teacher makes a multiple-choice quiz with 10 questions. 2 answers are A, 3 answers are B, 2 answers are C and 3 answers are D. How many possible answer keys are possible? 11) _____________________________ 2 marks 12. In a group of 14 students there are 8 girls and 6 boys. a) Determine the number of ways that a committee of 4 students can be chosen from this group. a) _____________________________ 1 mark b) Determine the number of ways that a committee of 4 students which has exactly 2 girls can be chosen from the group. b) ____________________________ 2 marks c) Determine the number of ways that a committee of 4 students which has at least 1 boy can be chosen from the group. c) ____________________________ 2 marks Version 1 2012 Page 6 of 13 Unit 7 Pre-Calculus 12 Unit 7 Send-In Assignment On-Line Course d) The committee of 4 students must have 1 girl and 1 boy and 2 other students, how many different committees can be chosen from this group? d) _____________________________ 2 marks 13.) Consider a standard deck of 52 cards. How many 5-card hands can be formed that include: a) only diamonds a) _____________________________ 2 marks b) exactly 3 face cards b) _____________________________ 2 marks Version 1 2012 Page 7 of 13 Unit 7 Pre-Calculus 12 Unit 7 Send-In Assignment On-Line Course c) at most 2 Queens c) _____________________________ 2 marks d) exactly 2 pairs (example 2 Queens, 2 Kings) d) _____________________________ 2 marks 14. Write the following expression without using the factorial symbol. n 4 ! n 2 ! 14. _____________________________ 2 marks Version 1 2012 Page 8 of 13 Unit 7 Pre-Calculus 12 15. Unit 7 Send-In Assignment On-Line Course Solve the following equations algebraically for n . *Show working using factorial notation. a) n! 3 4! n 2 ! a) _____________________________ 2 marks b) 9 Pr 15 120 *show working using factorial notation. b) _____________________________ 2 marks Version 1 2012 Page 9 of 13 Unit 7 Pre-Calculus 12 16. Unit 7 Send-In Assignment On-Line Course How many different paths can a ball take as it falls from top to bottom. 16. _____________________________ 2 marks 17. Find the number of pathways from A to B if you can only travel to the right and down. 17) _____________________________ 2 marks Version 1 2012 Page 10 of 13 Unit 7 Pre-Calculus 12 18. For 2a Unit 7 Send-In Assignment On-Line Course 3 : 8 a) how many terms are in the expansion. a) _____________________________ 70 1 mark b) determine the middle term of the expansion. b) _____________________________ 2 marks 19. Determine the first four terms of the expansion a b . 12 19. _____________________________ 2 marks Version 1 2012 Page 11 of 13 Unit 7 Pre-Calculus 12 20. Unit 7 Send-In Assignment On-Line Course Expand 3a 2 . 4 20. _____________________________ 3 marks 21. Determine the sixth term in the expansion a 413 . 21. _____________________________ 3 marks Version 1 2012 Page 12 of 13 Unit 7 Pre-Calculus 12 Unit 7 Send-In Assignment On-Line Course n 22. 1287 8 1 The sixth term of the expansion of x is x . Determine n . 3125 5 22. _____________________________ 3 marks 8 23. 1 5 Which term in the expansion of 3 x is a constant? 2x 23. _____________________________ 3 marks Version 1 2012 Page 13 of 13 Unit 7