Task:

- Read the attached math worksheet and finish all the questions.

REVIEW ASSIGNMENT COMBINATORICS Name: Teacher: School: Total = % 57 Formulae n! n! r!(n - r)! *k + 1 = n Gran -kbk (n - r)! n Cp = Page 1 of 10Show 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 6 digit house numbers would be even? (note: 0351 is not considered a house number and you only use each number once). 2 marks b) Using the same digits as above, how many 4 digit numbers smaller than 3500 could you form if repetition was not allowed? (note: 0351 is not considered a house number). b) 2 marks Page 2 of 10 Determine all the possible permutations of all the letters in FACTOR. 3) 1 mark 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 How many ways can 5 teddy bears, 6 toy trucks, 5 dolls and 1 toy car be distributed among 17 children if each child is to receive 1 item? 5) 2 marks Page 3 of 10 How many permutations can be formed from the letters in the word BANANAS if each arrangement must start and end with a n? *use factorial notation to determine the number of permutation. 6) 2 marks In how many ways can a school president, a vice-president, and a secretary be selected from the 11 students comprising the student council? 7) 2 marks Seven people attend a movie together. There are only 5 seats available in a row. In how many ways can 5 of the seven people be seated? 8) 2 marks Page 4 of 10 9. The coach from a soccer team of 15 players must select 11 players for the start of a game. a) Ofthe 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 dormitory at a local school has 4 rooms that contain 2, 3, 4, and 6 beds respectively. How many ways can 15 students be assigned to these rooms? 10) 2 marks Page 5 of 10 11. A teacher makes a multiple-choice quiz with 12 questions. 3 answers are A, 3 answers are B, 2 answers are C and 4 answers are D. How many possible answer keys are possible? 11) 2 marks In a group of 16 students there are 10 girls and 6 boys. a) Determine the number of ways that a committee of 5 students can be chosen from this group. a) 1 mark b) Determine the number of ways that a committee of 5 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 5 students which has at least 1 boy can be chosen from the group. c) 4 marks Page 6 of 10 13.) Consider a standard deck of 52 cards. How many 5-card hands can be formed that include: Clubs Diamonds Hearts Spades a) only diamonds a) 2 marks b) exactly 3 face cards b) 2 marks c) at most 2 Queens ) 2 marks Page 7 of 10 d) exactly 2 pairs (example 2 Queens, 2 Kings) d) 3 marks 14.) Write the following expression without using the factorial symbol. (n -4)! a) 3! (n - 2)! a. 2 marks b ) C3 + , C2 + n 91 b. 3 marks Page 8 of 10Solve the following equations algebraically for n. *Show working using factorial notation. a) 3 marks b) P, =84 C, *show working using factorial notation. b) 4 marks Page 9 of 10 16. List two similarities and two differences between permutations and combinations. (2 marks) Similarities Differences Page 10 of 10