Number of Subsets Containing a Set of Elements | Set Theory, Combinatorics

How do we count the number of subsets that contain a particular collection of elements? We'll be answering this question with an example and a general solution in today's video set theory lesson!

SOLUTION TO PRACTICE PROBLEM:

There are 4 elements of S, so S has 2^4 subsets total. How many subsets contain y and z? Well, to make such a subset we have one choice for y and z (to include each of them) and 2 choices for w and x, so the total number of subsets of S containing y and z is 2^(4-2) = 2^2 = 2*2 = 4. Let's list them: {y, z}, {y, z, x}, {y, z, w}, {y, z, w, x}.



I hope you find this video helpful, and be sure to ask any questions down in the comments!

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