Given a set s how many subsets of s contain at most 2 elements

Given a set S of cardinality , the subsets containing at most 2 elements are:

There is clearly only one empty set, and there are subsets containing one element (you choose one of the n elements in S to create your subset)

Finally, the number of subsets containing two elements is

In fact, in general, the binomial coefficient represents the number of subset of cardinality k that you can build from a set with cardinality n.

So, if we update our list, we have the following subsets:

For a total of

subsets with at most two elements.

third option: 6x+8

step-by-step explanation:

we can see that the given question is a sum of series and the values of n vary from 0 to 3

the first term will be:

when n=0, [(0)*x+2] => (0+2) => 2

when n=1, [(1)*x+2] => (x+2) => x+2

when n=2, [(2)*x+2] => 2x+2

when n=4, [(3)*x+2] => 3x+2

so adding up all the terms will give us:

=2+x+2+2x+2+3x+2

=x+2x+3x+2+2+2+2

=6x+8

so,

third option is the correct answer ..

75

step-by-step explanation: