1. MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

2. Lesson 10: Combinations

3. When different orderings are not to be counted separately, i. e
When different orderings are not to be counted separately, i.e. the outcome, mn is equivalent to the outcome nm, the problem involves combinations.

4. 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).

5. 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).

6. 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?

7. 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

8. Calculate the value of 7C4.

9. Calculate the value of 7C4
Calculate the value of 7C4. This represents a combination of 7 objects taken 4 at a time and is equal to

10. Calculate the value of 7C4
Calculate the value of 7C4. This represents a combination of 7 objects taken 4 at a time and is equal to

11. Calculate the value of 9C5

12. Calculate the value of 9C5 This represents a combination of 9 objects taken 5 at a time and is equal to . . .

13. Calculate the value of 9C5 This represents a combination of 9 objects taken 5 at a time and is equal to . . .

14. 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? 

15. 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

16. 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

17. Fini!