5. a) How many five-digit numbers can you form with the digits 1, 2, 3, 4, 5, 6, 7and 8 if no digit is repeated? b) How many ofthese fivedigit numbers are odd numbers? (4 marks) 6. A family has 5 children. Assuming that the chance of a boy or girl is equally likely, what is the probability of family arrangements that have: a) exactly 3 girls? b) no girls? c) at least 2 girls? (6 marks) 7. Given that a 13-card bridge hand has been dealt from a standard deck of 52 cards, what is the probability of having: a) exactly 5 hearts? b) exactly 7 hearts, 3 diamonds, 2 clubs, and 1 spade? (4 marks) 8. How many different arrangements of 7 letters can be formed from the word PROBLEM if: a) no letter can be repeated? b) no letter can be repeated and the arrangements must start with the letter P? c) no letter can be repeated and the "P\" and the "R\" must be together? (6 marks}