[Komkanit]

1.Three sets have 5, 10, and 15 elements, respectively. How many elements can their union and their intersection have?
2.Let B be a subset of A, |A| = n, |B| = k. What is the number of all subsets of A whose intersection with B has 1 element?
3.Compute the binary form of 25 and 35, and compute their sum in the binary notation. Check the results against adding 25 and 35 in the usual decimal notation and then converting it to binary.
4.Starting from Washington, DC, how many ways can you visit 5 of the 50 state capitals and return to Washington?
5.You want to send postcards to 12 friends. In the shop there are only 3 kinds of postcards. In how many ways can you send the postcards, if
(a) there is a large number of each kind of postcard, and you want to send one card to each friend;
(b) there is a large number of each kind of postcard, and you are willing to send one or more postcards to each friend (but no one should get two identical cards);
(c) the shop has only 4 of each kind of postcard, and you want to send one card to each friend?
6. What is the number of ways to color n objects with 3 colors if every color must be used at least once?
7. How many different ?words? can you get by rearranging the letters in the word MATHEMATICS?

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