Probability

In the following problem give your answer using the notation nPr or nCr. You don’t have to give an actual numerical answer.
There are 10 athletes entered in a race. If a gold, silver, or bronze medal is given to three of the athletes, in how many ways can one pick the winners of the gold, silver, and bronze medals?
There are 10 athletes entered in a race. If three identical gold medals are given to the group of athletes, in how many ways can one pick the winners of the gold medals?
A card is drawn out of a standard deck of 52 cards. Each card can be described by giving its “rank” (A, 2, 3, 4,…10, J, Q, K) and its “suit” (H for hearts, C for clubs, D for diamonds, and S for spades). For example, 2S denotes the two of spades and KH denotes the king of hearts. Write out the event described by each of the following statements as a set.
E1: “draw a king.”
E2: “draw a heart.”
E3: “draw a face card.” (A “face” card is a jack, queen, or king.)
A card is drawn at random out of a well-shuffled deck of 52 cards. Find the probability of each of the following events. (Do problem #2 first.)
E1: “draw a king.”
E2: “draw a heart.”
E3: “draw a face card.” (A “face” card is a jack, queen, or king.)
Out of 420 students who took a statistics test, 260 passed. What percentage of the students passed the test?
An employee’s hourly wage increased from $11.00 per hour to $13.50 per hour. What is the percentage increase in their wage?
Suppose that you deposit $3,250.00 in a savings account that pays 0.4% annual simple interest.
Assuming no withdrawals are made, find the balance in the account after 6 years.
Round your answer to the nearest penny.
Suppose that you deposit $3,250.00 in a savings account that pays 0.4% annual interest, with interest credited to the account at the end of each year. Assuming no withdrawals are made, find the balance in the account after 6 years. Round your answer to the nearest penny.
Suppose $3,250.00 is invested in a savings account with an APR of 0.4% compounded monthly. Assuming no withdrawals are made, find the balance in the account after 6 years. Round your answer to the nearest penny.