A universal set U with 66 elements has been partitioned into three subsets, A, B, and C. If B is 2 times the size of A and C is 4 times the size of B, then how many elements are in B?

A student works in a bookstore where he is required to work at least four and at most five days a week, at least one of which has to be a weekend day (Saturday or Sunday). How many different weekly work schedules can this student have?

Consider a popular ramen stall. Before the shop opens, there are 20people waiting in front of the restaurant.    Given that the shop only serves 10 bowls per day. If the maximum number ofeach menu the customers can order is 7 which means if the first 7 people orderShoyu Ramen, the rest must order Seafood Ramen. How many combinationof ramen orders(how each customer order and who got kicked out) are there?Ex: People can still order 5 Shoyu and 5 Seafood if they wish. But, no, the10 people who gets in can’t order 8 Shoyu and 2 Seafood.

A 100-page document is being printed by four printers. Each page will be printed exactly once. Suppose that the first and the last page of the document must be printed in color, and only two printers are able to print in color. The two color printers can also print black-and-white. How many ways are there for the 100 pages to be assigned to the four printers. Hint: Use the product rule.