6. A bakery produces five types of bagels, two of which are chocolate chip and cinnamon raisin. (a) If there are at least 12 bagels of each type, how many different selections of 12 bagels are there? (b) Suppose there are only four chocolate chip and three cinnamon raisin bagels, but at least 12 of the other three types. How many different selections of 12 bagels are there? 7. Use mathematical induction and Pascal's formula to prove that for every integer every integer n 2 0, 8. Prove for every integer n 20. 4" - ( 8 )+3( 7 )+3-( 3 )+ +3- ( = )- 9. One jar contains 14 red candies and 10 green candies, and a second jar contains 9 red candies and 21 green candies. A jar is selected at random, and a candy is chosen from the jar. (a) What is the probability that the chosen candy is red? (b) If the chosen candy is red, what is the probability that it came from the second jar? 10. A test for a virus is used in a population in which 3% have the virus. Suppose the false positive rate is 4% and the false negative rate is 2%. (a) What is the probability that a randomly chosen person has the virus and tests positive? (b) What is the probability that a randomly chosen person who tests positive actually has the virus