Please enter your initials here (7) Numerical Response - 1 mark per blank. 6. How many four-digit codes are possible using the digits 0 through 9 a) if digits can be repeated? b) with no repeated digits? codes codes 7. Simi draws a single card from a standard deck of playing cards. How many possibilities does she have to draw a) either an ace or a red face card? b) either a heart or a 9? possibilities possibilities 8. a) A president, a vice-president, and secretary from a council of 10 students can be chosen in ways. b) A subcommittee of 4 from the remaining 7 students can be chosen in ways. 9. different arrangements of the letters in the word SEQUENCES are possible. Written Response: Show your work for full marks. 10n! (4) 10. Solve for n, and state the restrictions.- ( 72 + 1 ) ! = 2Please enter your initials here (5) 11. Yelena rolls a die and tosses two coins, a loonie and a toonie. a) Draw a tree diagram and use it to determine the total number of outcomes Yelena could achieve. b) Use the Fundamental Counting Principle to verify your answer to part (a). Show your work. c) Based on the tree diagram, how many outcomes are possible for which Yelena rolls a multiple of 3 or gets at least one tail? Page 4 of 5Please enter your initials here (6) 12. Neil is creating an 8-character password. More than half of the characters will be lowercase letters, and the rest will be digits from 0 to 9. Neil will use at least one digit and will not use any character more than once. The digits will follow the letters. Note: the characters (digits and letters) will not be not be used more than once. a) Describe three different cases for this problem. b) How many passwords are possible if in each password the digits follow the letters? (3) 13. Twelve camp counselors are signing up for training courses that have only a limited number of spaces. Only five people can take the water safety course, three people can take the first aid course, two people can take the conflict management course and two people can take the astronomy course. How many ways can the 12 counselors be placed in the four courses? Page 5 of 5