16. Use mathematical induction to prove the formula 3n(a + 1) 3+6 +9+ . . . + 30 = 2 17. Use the Binomial Theorem to expand and simplify (20 - 56)4. In Exercises 18-21, evaluate the expression. 18. .C 19- 20 3 20. , P2 21. 76 P3 22. Solve for n in 4 . P, = .. . ,P.. . 23. How many distinct license plates can be issued consisting of one letter followed by a three-digit number? 24. Four students are randomly selected from a class of 25 to answer questions from a reading assignment. In how many ways can the four be selected? 25. A card is drawn from a standard deck of 52 playing cards. Find the probability that it is a red face card. 26. In 2006, six of the eleven men's basketball teams in the Big Ten Conference were to participate in the NCAA Men's Basketball Championship Tournament. If six of the eleven schools are selected at random, what is the probability that the six teams chosen were the actual six teams selected to play? 27. Two integers from 1 to 60) are chosen by a random number generator. What is the probability that (a) both numbers are odd. (b) both numbers are less than 12, and (c) the same number is chosen twice? 28. A weather forecast indicates that the probability of snow is 75% . What is the probability that it will not showIn Exercises 1-3, use a graphing utility to graph the function and approximate the limit (if it exists). Then find the limit (if it exists) algebraically by using appropriate techniques. - 1. lim 2. lim -1 + 5x - 3 3. lim VG - 2 2x 1 - x X - 5 In Exercises 4 and 5, use a graphing utility to graph the function and approximate the limit. Write an approximation that is accurate to four decimal places. Then create a table to verify your limit numerically. sin 3x 4. lim 5. lim