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Welcome to the guide on Permutations and Combinations

Please note this topic is a big differentiator in getting a high score.

*PATH2TJ approved use only*

The prerequisites are a thorough understanding of Factorials. If you do not have a good handle on these concepts, use the links below to explore these concepts and skills first. Though this topic is often taught in schools, it is not always covered to the depth necessary to quickly answer questions. This lesson will focus on the specifics of permutations and combinations to the level needed for the test.

Choose one or more of the following links to come up to the speed with the concepts:

https://betterexplained.com/articles/easy-permutations-and-combinations/ (The first site to visit giving a basic introduction)

https://youtu.be/6B-dvOMTeV8?t=44 (A short video to bring you up to speed) https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb#x9e81a4f9838 9efdf:combinatorics-precalc (A classic site to learn and test yourself)

https://youtu.be/wJDKqEYq7SY (A short video on combinations)

https://youtu.be/p8vIcmr_Pqo (A longer, in-depth video on combinations) https://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/index.html (Use tutorials 55,56, and 57 to attain a college-level understanding)

Practice and check your understanding with the practice sheets available here:

https://leagueland.typepad.com/files/ws-1---counting-combinations-permutations-key.pdf (A question bank with any questions, do enough to make you feel comfortable) https://mi01000971.schoolwires.net/cms/lib/MI01000971/Centricity/Domain/429/Permutations% 20and%20Combinations%20Worksheet.docx (Practice problems to learn Permutations and Combinations. HIGHLY RECOMMENDED THAT YOU DO ALL OF THESE) https://mi01000971.schoolwires.net/cms/lib/MI01000971/Centricity/Domain/429/Permutations% 20and%20Combinations%20Worksheet%20KEY.pdf (Answers to the questions above)

Now check if you are battle-ready by answering the following questions:

1. A letter lock Consists of four rings, each ring contains 9 digits. The lock can be opened by setting a four-digit code with the correct combination of the four rings. How many unsuccessful attempts are possible in which the lock cannot be opened?

a. 4 9 -1

b. 9 4 -1

c. 9C4

d. None of the above

2. In how many ways can 11 identical books on English and 9 identical books on Math be placed in a row on a shelf so that two books on Math are not together?

a. 110

b. 220

c. 330

d. 440

3. There are 6 numbered chairs placed around a circular table. 3 boys and 3 girls want to sit on them in a way that no two boys nor girls sit next to each other. How many such arrangements are possible?

a. 36

b. 58

c. 72

d. None of the above

4. A committee is to be formed in which 5 people are chosen from 6 men and 4 women is to be chosen. In how many ways can this committee be made if there can be, at most, 2 women? a. 186 b. 168 c. 136 d. 169 5. Allen and Mary host a TV show together in which one day N number of guests attend the show. Each guest shakes hands with every other guest and each guest also shakes hands with each host. If there happens to be a total of 65 handshakes, find the number of guests that attended the show.

a. 13

b. 14

c. 10

d. 9

6. If 10 objects are arranged in a row, then the number of ways of selecting three of these objects such that no two of them are adjacent is:

a. 56

b. 65

c. 28

d. 13

7. 8 people are to be seated at Melville's Restaurant. The only table available is a round table. However, Jack and Jill insist on sitting next to each other. In how many ways can the 8 people be seated?

a. 8!

b. 8 + 3!

c. 7!

d. 6! + 2

8. Suppose the Lincoln-Douglas debate team consists of 10 seniors. Two of which will be randomly selected to become captains. However, one of the seniors is already captain of another club and is ineligible. In how many ways can the two captains be chosen?

a. 36

b. 72

c. 45

d. 90

9. Oliver is applying for an internship and says, “I have a 15% chance of being accepted to Internship A and I have a 5% chance of getting accepted into both A and B. Assuming Oliver will be accepted by at least one internship, what is the chance he is accepted for internship B but not A?

a. 15%

b. 65%

c. 80%

d. 20%

Answer key:

1. B

2. B

3. C

4. A

5. C

6. A

7. D

8. A

9. C

Congrats on reaching the end of this lesson. If you did not understand any concept be sure to go back through and review, so that you can be fully prepared. We learn the most from our mistakes so don’t be disheartened by them. When you feel that you are ready, go ahead and take a little break. Then come back and move onto another section!