The questions are to be answered with full solutions. Be sure to focus on proper mathematical form, including:
1. One equal sign per line,
2. Equal signs in each question lined up vertically with each other,
3. No self-developed short form notations,
4. One step or idea per line,
5. Show complete solution to the given problem.
1. Jesse has collected 24 baseball cards. Use combinations to find the number of ways to choose 5 to put on the cover of his album.
2. In how many ways can you have a snack if you find 3 apples, 2 bananas and 4 cookies on the kitchen counter?
3. How many different sums of money can you make with a penny, a nickel and a quarter?
4. Solve the following equation for n, where n is a natural number.
C (n+1, 3) = C(n,2)
5. A theme park has a variety of rides. There are 7 roller coasters, 4 water rides and 9 story rides. If Melanie wants to try one of each type of ride, how many different combinations or rides could she choose?
6. A box contains 6 blue socks and 4 white socks. Find the number of ways 2 socks can be drawn from the box where:
a. there are no restrictions
b. they are different colors
c. they are the same color
7. Given an example of a situation in which you would use the formula:
(p+1)(q+1)(r+1) .-1 . Explain why this formula applies in your example.
8. A teacher organizing a field trip finds that 50 students have signed up. However, the bus has only 47 seats, so a few students will have to travel by car. The teacher and one other supervisor must go on the bus. Explain two different methods for using combinations to find how each teacher can choose which students go on the bus. Show that both methods produce the same answer.