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College Mathmatics - Subsets

Determine the number of subsets of {mom, dad, son, daughter}

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Jul 24, 2011
Determine Number of Subsets
by: Staff

The question:

Determine the number of subsets of {mom, dad, son, daughter}

The answer:

Generally speaking, the order of elements within a set does not matter. I assume this will be true for your question.

n = number of elements in the set

Number of possible subsets = 2ⁿ

Number of subsets for {mom, dad, son, daughter}

n = 4

Number of possible subsets = 2⁴
Number of possible subsets = 16

You can also determine how many of these subsets have 1 element, two elements, etc., by calculating the binomial coefficient:

combination notation

n = number of objects

k = number of objects taken at a time

n_C_k can be read “n objects taken k at a time”

n_C_k = (n!/k!)*[1/(n-k)!]

The subsets are:

1 Null Set (an empty set):

n_C_k = (n!/k!)*[1/(n-k)!]

4_C_0 = (4!/0!)*[1/(4-0)!]

4_C_0 = 1

{ }

4 Proper Subsets containing only 1 element:

4_C_1 = (4!/1!)*[1/(4-1)!]

4_C_1 = 4

{mom}, {dad}, {son}, {daughter},

6 Proper Subsets containing two elements:

4_C_2 = (4!/2!)*[1/(4-2)!]

4_C_2 = 6

{mom, dad}, {mom, son}, {mom, daughter},
{dad, son}, { dad, daughter},
{son, daughter},

4 Proper Subsets containing three elements:

4_C_3 = (4!/3!)*[1/(4-3)!]

4_C_3 = 4

{mom, dad, son}, {mom, dad, daughter}, {mom, son, daughter}
{dad, son, daughter},

1 Improper Subset containing all four elements:

4_C_4 = (4!/4!)*[1/(4-4)!]

4_C_4 = 1

{mom, dad, son, daughter}

Total number of subsets (all categories): 16

Thanks for writing.


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