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# G7

last edited by 14 years, 1 month ago

lena

Combinations and permutations refer to how many different ways a specific number of things can be selected from a larger group. For example how many different groups of 3 letters can be selected form the group ABCDE.

The difference between combinations and permutations is as follows:

Combinations:

In combinations, the order in which the items appear

in the selected group does not matter.

for example the grouping:     ACE                                                                              Permutations

would be considered the same as:  EAC

In permutations,the order in which the items appear in the selected

because they both contain the same letters                                                             group does matter.

The total different ways a combination of 3 could be taken from the                        For example the grouping:  bed

group of letters ABCDE:

would be conidered a different group from:  bde

ABC         BEA

ACD         DBA                                                                                                             The total number of different ways a permutation could be

ADE         BCE                                                                                                              taken from a group would be much greater than the number

BCD         DEC                                                                                                             of combinations. for example the total different ways that a

ACE             BDE                                                                                                                                                  permutation of three could be taken from a group of 5 is

The equation for finding how many combinations can be made is:

The equation for how many permutations can be made is:

where: n=total numer of things to be

selected from (in this case 5)                                               Where: n=total number of things to

be selected from

r=number of letters selected for

combination (in this case 3)                                                                                     r=number of letters selected

for permutation

!=a number is multiplied by all numbers

smaller than it down to 1 (5!=5x4x3x2x1)                                                               !=a numer is to be multiplied

by all numbers smaller than

it down to 0

In both cases each combination can only use each available option once. For example, AAB would not be considered a combination

or permutation.

Sample Question:

1. an orchestra is auditioning for a new bassoon section of 4. If 7 bassoons audition, how many different bassoon sections could result?

Answer:

n=7(number of bassoons to be auditioned)

r=4(number of bassoons that make up the section)

35 possible bassoon sections could result

2.  In the same bassoon section, there are positions of 1st, 2nd, 3rd, and 4th to be auditioned for. how many

different sections could result?

Answer:

840 possible sections could result.

### Comments (1)

#### Anonymous said

at 7:35 pm on Jun 14, 2007

Nice work Lena. A table might help to keep your permuations and combinations sections organized.

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