MATHCOUNTS TOOLBOX
Facts, Formulas and Tricks
Lesson 10: Combinations
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.
This represents a combination of 7 objects
taken 4 at a time and is equal to
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
Fini!