Prompt: Each time you enter a guess, the program will tell you whether the secret word is alphabetically before your guess, alphabetically after your guess, or exactly matches your guess. Each secret word is randomly chosen from a dictionary with exactly 267, 751 words. Question: Suppose I give you $15 to play the online Guess My Word game. Every time you make a guess, you give me $1. If you agree to play this game with me, do you expect to win money or lose money? Clearly justify your answer. (Assume that each of the 267, 751 words is equally likely to be chosen.)

If a man has 4 sweaters and 5 pairs of slacks, how many different outfit can he wear?

In horse racing, a “trifecta” occurs when a bettor wins by selecting the first three finishers in the exact order (1 St place, 2nd place, and 3rd place). How many different trifectas are possible if there are 14 horses in a race?

Pet Owners According to the Humane Society, in 2015, 65% of U.S. households owned at least one pet, and 42% of households who did own pets owned at least two. The U.S. Census Bureau tells us that there were 117 million households in 2015. How many households owned at least two pets? Report your answer in millions rounded to two places.

Over the past year, John has purchased 30 books. In how many ways can he pick four of these books and arrange them, in order, on his nightstand bookshelf? In how many ways can he choose four of these books to take with him on his vacation at the shore?

Visa cards have 16 digits. The first digit is always 4 as in 4xxxxx – with the 2nd to 6th digits being the bank number while the 7th-15th numbers are your account number. The final digit is the check digit.   How many possible Visa card numbers are available?

A student needs to answer 20 out of 30 questions on a test. Find the number of ways the student can choose if the student must answer the first 8 questions on the test.

On valentine's day, the Quiet Nook restaurant offers a Lucky Lovers Special that could save couples money on their romantic dinners. When the waiter brings the check he also brings a scratch-off ticket that the couple scrapes to reveal a hidden number; call this number X. The value of the number X is the dollar amount that will be subtracted from the dinner bill. The possible values of the scratch-off number X are shown in the table below. The table also shows the probability distribution of the values of X. a) for the past several weeks, the restaurant has also been distributing coupons worth $5 off any dinner for two. The coupon can be used in addition to the discount X from the scratch-off ticket. If every couple dining there on Valentine's Day also brings a $5 coupon, what are the expected value and standard deviation of the total discount the couples receive?