MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

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MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

Lesson 10: Combinations

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.

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).

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).

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?

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

Calculate the value of 7C4.

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

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

Calculate the value of 9C5

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

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

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?

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

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

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