How many subsets of size 4 are there?

Question

All I can think of is there are $2^8$ subsets of the set. Then, there are $2^5$ subsets of size $5.$ So $2^8-2^5$ gives you the number of subsets of four elements. How do I even approach this problem?

Answer 1

Hint: Make a grid where the rows are labeled one to eight, and the columns are labeled with the subsets. Place a check mark in a box if the subset at that column contains the number at that row. Then every row has three check marks, and every column has four...