For problems #1-5 determine if a permutation or combination is appropriate.
1. Determining the number of ways \(4\) people can line up.
2. Determining the number of ways two people can be selected for a tennis doubles team out of \(11\) players.
3. Determining the number of ways 1st, 2nd, and 3rd place can be decided in a tournament of \(32\) teams.
4. Determining the number of ways \(12\) people can be picked for a jury out of \(30\) people.
5. Determining the number of triangles can be formed from \(10\) non-collinear points.
6. Give a situation in which a permutation can be applied.
7. Give a situation in which a combination can be applied.
For problems #8-12 compute each expression by hand
8. \(_4 P _2\)
9. \( _{10} C _6\)
10. \(\large\frac{130!}{126!}\)
11. \(_4 C _0\)
12. \(_{10} P _6\)
13. Determine the answer to the situation in #1.
14. Determine the answer to the situation in #2.
15. Determine the answer to the situation in #3.
16. Determine the answer to the situation in #4.
17. Determine the answer to the situation in #5.
18. An Illinois license plate is two letters followed by four digits. The first of the digits cannot be a zero and the second letter cannot be an A. How many different license plates are possible?
19. How many four digit pin codes are possible if the digits can be repeated?
20. How many four digit pin codes are possible if the digits cannot be repeated? How does this compare to the previous result? Write a logical explanation for the difference between these two scenarios.
21. How many distinguishable permutations are there of the letters in the word INTEGRATION ?
22. On a quiz consisting of \(8\) true false questions followed by \(10\) multiple choice questions (each of which has four options) how many different ways are there to complete the quiz?
23. When shopping for a new car you see that there are \(3\) different trim lines, \(8\) different colors, and \(7\) different interior packages. How many different options are there for this type of car?
24. If you have \(4\) tickets to a concert and \(9\) friends, how many different groups can attend the concert? You must be in on of these groups, they're your tickets!
25. If \(a+b=n\) prove that \(_n C _a = _n C _b\) for positive integers \(n\), \(a\), and \(b\).
Review Problems
26. What is the period of \(f(x)=-3 \cos (2 \pi x)-8\)?
27. Evaluate \(\sec (\frac{3 \pi}{2})\).
28. Evaluate \(\sum\limits_{k=1}^{\infty} 2(\frac{3}{4})^{k-1}\).
29. Find the length of an arc subtended by an angle measuring \(130 ^{\circ}\) with a radius of \(4\) ft.
30. Where does the graph of \(f(x)= \ln x\) cross the y-axis?
Solution Bank