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Magazine Problem 8
Find the \(n\) th term, the fifth term, and the elghth term of the geometric sequence. $$2,6,18,54, \dots$$
Problem 16
Find all possible values of \(r\) for a geometric sequence with the two given terms. $$a_{3}=4, a_{7}=\frac{1}{4}$$
Problem 16
Determine the number of positive integers less than \(10,000\) that can be formed from the digits \(1,2,3,\) and 4 if repetitions are allowed.
Problem 19
Suppose five cards are drawn from a deck. Find the probability of obtaining the indicated cards. If Four of a kind (such as four aces or four kings)
Problem 22
Suppose five cards are drawn from a deck. Find the probability of obtaining the indicated cards. Five face cards
Problem 22
Tossing dice Two dice are tossed, one after the other. In how many different ways can they fall? List the number of different ways the sum of the dots can equal (a) 3 (b) 5 (c) 7 (d) 9 (e) 11
Problem 29
Basketball championship series The winner of the seven game NBA championship series is the team that wins four games. In how many different ways can the series be extended to seven games?
Problem 34
After selecting nine players for a baseball game, the manager of the team arranges the batting order so that the pitcher bats last and the best hitter bats third. In how many different ways can the remainder of the batting order be arranged?
Problem 35
Five cards are drawn from a deck. Find the probability of the specified event. Obtaining at least one ace
Problem 35
Express the sum in terms of summation notation and find the sum. $$8+19+30+\dots+16,805$$
