91Ó°ÊÓ

Solve by the method of your choice. From a club of 20 people, in how many ways can a group of three members be selected to attend a conference?

What is true about the sum of the exponents on \(a\) and \(b\) in any term in the expansion of \((a+b)^{n} ?\)

A company offers a starting yearly salary of \(\$ 33,000\) with raises of \(\$ 2500\) per year. Find the total salary over a ten-year period.

You are considering two job offers. Company A will start you at \(\$ 19,000\) a year and guarantee a raise of \(\$ 2600\) per year. Company B will start you at a higher salary, \(\$ 27,000\) a year, but will only guarantee a raise of \(\$ 1200\) per year. Find the total salary that each company will pay over a ten- year period. Which company pays the greater total amount?

A deposit of \(\$ 6000\) is made in an account that earns \(6 \%\) interest compounded quarterly. The balance in the account after \(n\) quarters is given by the sequence $$a_{n}=6000\left(1+\frac{0.06}{4}\right)^{n}, \quad n=1,2,3, \ldots$$ Find the balance in the account after five years. Round to the nearest cent.

A section in a stadium has 20 seats in the first row, 23 seats in the second row, increasing by 3 seats each row for a total of 38 rows. How many seats are in this section of the stadium?

Use the formula for the sum of the first \(n\) terms of a geometric sequence to solve. You save \(\$ 1\) the first day of a month, \(\$ 2\) the second day, \(\$ 4\) the third day, continuing to double your savings each day. What will your total savings be for the first 15 days?

Make Sense? In Exercises \(66-69\), determine whether each statement makes sense or does not make sense, and explain your reasoning. Suppose that it is a drawing in which the Powerball jackpot is promised to exceed \(\$ 700\) million. If a person purchases \(292,201,338\) tickets at \(\$ 2\) per ticket (all possible combinations), isn't this a guarantee of winning the jackpot? Because the probability in this situation is 1, what's wrong with doing this?

A job pays a salary of \(\$ 24,000\) the first year. During the next 19 years, the salary increases by \(5 \%\) each year. What is the total lifetime salary over the 20 -year period? Round to the nearest dollar.

a. If two people are selected at random, the probability that they do not have the same birthday (day and month) is \(\frac{365}{365} \cdot \frac{364}{365}\). Explain why this is so. (Ignore leap years and assume 365 days in a year.) b. If three people are selected at random, find the probability that they all have different birthdays. c. If three people are selected at random, find the probability that at least two of them have the same birthday. d. If 20 people are selected at random, find the probability that at least 2 of them have the same birthday. e. How large a group is needed to give a 0.5 chance of at least two people having the same birthday?