Homework problems

Problem5. A sum of 15 cents was paid by two coins, and one of these two coins was not a nickel. Find the values of the coins
Problem6. In a box, there are pencils of at least 2 different colors and of 2 different sizes. Prove, that there are 2 pencils that differ both in color and in size.
Problem7. Three people -- A, B and C -- are sitting in a row in such a way that A sees B and C, B sees only C, C sees nobody. They were shown 5 caps -- 3 red and 2 white.They were blindfolded and three hats were put on their heads. Then the blindfolds were taken away and each of the people was asked if they could determine the color of their caps. After first A, and then B, answered negatively, C answered positively. How was that possible?