Combinatorics | Number Theory Answers

ABCD is a convex quadrilateral . 3,4,5 & 6 points are marked on he sides AB,BC,CD &DA ,respectively .What is the number of triangles with vertices on different sides.

Pam and sipho are playing cards. They take it in turns to remove one, two or three cards from the pack, they may remove the same number of cards as the previous player. For example, if pam removes three cards then sipho can only remove one or three cards and so on. The winner of the game is the person who takes either the last card, or leaves the other player with no valid moves. For the investigation suppose that pam always starts first and both pam and sipho play to win. Answer the following questions: (a) investigate who would win if the pack of cards has as many as 13 cards in it. (B) who would win with a pack of 15cards? Explain fully. (C) who would win with a pack of 16cards? (D) who would win if sipho and pam play with a full pack of 52, or even 99 cards?

An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 96 students in the school. There are 37 in the Spanish class, 31 in the French class, and 22 in the German class. There are 14 students that in both Spanish and French, 5 are in both Spanish and German, and 8 are in both French and German. In addition, there are 2 students taking all 3 classes. If two students are chosen randomly, what is the probability that at least one of them is taking a language class?

convert 5/13 into a recurring decimal using long division