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! ******************************************************************** The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work. Vallow Bandcamp: https://vallow.bandcamp.com/ Vallow Spotify: https://open.spotify.com/artist/0fRtu... Vallow SoundCloud:   / benwatts-3   ******************************************************************** +WRATH OF MATH+ ◆ Support Wrath of Math on Patreon:   / wrathofmathlessons   Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Music Channel:    / seanemusic