MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.
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Transcript of MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.
![Page 1: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/1.jpg)
MATHCOUNTS TOOLBOX
Facts, Formulas and Tricks
![Page 2: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/2.jpg)
Lesson 10: Combinations
![Page 3: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/3.jpg)
When different orderings are not to be counted separately, i.e. the
outcome, mn is equivalent to the outcome nm, the problem involves
combinations.
![Page 4: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/4.jpg)
Combination Formula:Different orders of the same items are not
counted. The combination formula is equivalent to dividing the corresponding
number of permutations by r!.n: number of available items or choices
r: the number of items to be selected Sometimes this formula is written:
C(n,r).
![Page 5: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/5.jpg)
Combination Formula:Different orders of the same items are not
counted. The combination formula is equivalent to dividing the corresponding
number of permutations by r!.n: number of available items or choices
r: the number of items to be selected Sometimes this formula is written:
C(n,r).
![Page 6: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/6.jpg)
Taking the letters a, b, and c taken two at a time, there are six permutations: {ab, ac, ba,
bc, ca, cb}. If the order of the arrangement is not important, how many of these outcomes are equivalent, i.e. how many combinations
are there?
![Page 7: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/7.jpg)
Taking the letters a, b, and c taken two at a time, there are six permutations: {ab, ac, ba,
bc, ca, cb}. If the order of the arrangement is not important, how many of these outcomes are equivalent, i.e. how many combinations
are there? ab = ba; ac = ca; and bc = cb
The three duplicate permutations would not be counted, therefore three
combinations exist
![Page 8: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/8.jpg)
Calculate the value of 7C4.
![Page 9: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/9.jpg)
Calculate the value of 7C4.
This represents a combination of 7 objects
taken 4 at a time and is equal to
![Page 10: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/10.jpg)
Calculate the value of 7C4.
This represents a combination of 7 objects
taken 4 at a time and is equal to
![Page 11: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/11.jpg)
Calculate the value of 9C5
![Page 12: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/12.jpg)
Calculate the value of 9C5
This represents a combination of 9 objects taken 5 at a time and is
equal to . . .
![Page 13: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/13.jpg)
Calculate the value of 9C5
This represents a combination of 9 objects taken 5 at a time and is
equal to . . .
![Page 14: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/14.jpg)
In how many ways can three class representatives be chosen from a group of twelve students? If the order of the
arrangement is not important, how many outcomes will there be?
![Page 15: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/15.jpg)
In how many ways can three class representatives be chosen from a group of twelve students? If the order of the
arrangement is not important, how many outcomes will there be?
This represents a combination of 12 objects taken 3 at a time and is equal to
![Page 16: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/16.jpg)
In how many ways can three class representatives be chosen from a group of twelve students? If the order of the
arrangement is not important, how many outcomes will there be?
This represents a combination of 12 objects taken 3 at a time and is equal to
![Page 17: MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 10: Combinations.](https://reader035.fdocuments.in/reader035/viewer/2022062404/551be021550346be588b5d7e/html5/thumbnails/17.jpg)
Fini!