1) Give clearly justified answers to the following.

a) How many 7-digit telephone numbers can be formed if the first digit cannot be 0 or 9 and if the last digit is greater than or equal to 2 and less than or equal to 3? Repeated digits are allowed.

b) How many different ways are there to arrange the 6 letters of the word CANDLE?

c)Tim writes the letters of his name on cards (one letter on each card) and puts them in a hat. He mixes up the cards and randomly picks a card out. He returns the card, mixes them up, and picks another card. He repeats this one more time. What is the probability that he picks the letters of his name (in the correct order)?

d)In how many ways can 12 people be placed on 3 distinct teams of 3, 5, and 4 members?

e)A contestant tosses a fair six-sided die. He receives $18 if a 3 appears and pays $3 if a number other than 3 appears. What is the expected value of a trial of this game?

f)suppose that a hand of 8 cards is dealt from a standard deck of cards. What is the probability that the hand has atleast one spade?