The trifecta at most racetracks consists of selecting the first-, second-, and third-place finishers in a particular race in their proper order. If there are seven entries in the trifecta race, how many tickets must you purchase to guarantee a win?

At a computer store, a customer is considering 5 different computers, 4 different monitors, 7 different printers, and 2 different scanners. Assuming that each of the components is compatible with one another and that one of each is to be selected, determine the number of different computer systems possible.

In one question on a history test, a student is asked to match 10 dates with 10 events; each date can be matched with only 1 event. In how many different ways can this question be answered?

In horse racing, a trifecta is a bet that the first three finishers in a race are selected in the correct order. In a race with 12 horses, how many different trifecta bets are possible? If you randomly guess the order of the first three finishers in a race with 12 horses, what is the probability of winning?

In how many ways can the digits in the number 2,142,332 be arranged?

In horse racing, one can make a trifecta bet by specifying which horse will come in first, which will come in second, and which will come in third, in the correct order. One can make a box trifecta bet by specifying which three horses will come in first, second, and third, without specifying the order. a. In an eight-horse field, how many different ways can one make a trifecta bet? b. In an eight-horse field, how many different ways can one make a box trifecta bet?

A swimming event has fifteen participants. The 4 swimmers with the fastest speeds will listed, in order, on the leader board. How many different ways are there for the names to be listed?

In how many ways can the digits in the number 4,568,865 be arranged?

A disc jockey (DJ) has 9 songs to play. Five are slow songs, and 4 are fast songs. Each song is to be played only once. In how many ways can the DJ play the 9 songs if (a) The songs can be played in any order? (b) The first song must be a slow song and the last song must be a slow song? (C) The first two songs must be fast songs?

Perform each of the following steps.
Use the traditional method of hypothesis testing unless the P-value method is specified by your instructor.
Trifecta Winnings A random sample of $\$1$ Trifecta tickets at a local racetrack paid the following amounts (in dollars and cents). Is there sufficient evidence to conclude that the average Trifecta winnings exceed $\$ 50$ ? Use $\alpha=0.10$. Assume the variable is normally distributed. \

$$\begin{array}{rrrr}8.90 & 141.00 & 72.70 & 32.40 \\ 70.20 & 48.60 & 75.30 & 19.00 \\ 15.00 & 83.00 & 59.20 & 190.10 \\ 29.10 & & & \end{array}$$

c. Compute the test value.

Suppose you toss a fair coin $100$ times, getting $42$ heads and $58$ tails, which is $16$ more tails than heads. a. Explain why, on your next toss, the difference between the numbers of heads and tails is as likely to grow to $17$ as it is to shrink to $15$. b. Extend your explanation from part (a) to explain why, if you toss the coin $1000$ more times, the final difference between the numbers of heads and tails is as likely to be larger than $16$ as it is to be smaller than $16$. c. Suppose you are betting on heads with each coin toss. After the first $100$ tosses, you are well on the losing side. Explain why, if you continue to bet, you will most likely remain on the losing side. How is this answer related to the gambler's fallacy?

In a horse race, a quinela bet is won if you selected the two horses that finish first and second, and they can be selected in any order. The 140th running of the Kentucky Derby had a field of 19 horses. What is the probability of winning a quinela bet if random horse selections are made?

use the trigonometric substitution to write the algebraic expression as a trigonometric function of θ, where 0 < θ < π2. √25-x^2, x = 5 sin θ

The Shroud of Turin shows the negative image of the body of a man who appears to have been crucified. It is believed by many to be the burial shroud of Jesus of Nazareth. In 1988 the Vatican granted permission to have the shroud carbon dated. Several independent scientific laboratories analyzed the cloth and the consensus opinion was that the shroud is approximately 660 years old, an age consistent with its historical appearance. This age has been disputed by many scholars. Using this age, determine what percentage of the original amount of C-14 remained in the cloth as of 1988.