Discrete Mathematics Answers

Suppose that in a bushel of 100 apples there are 20 that have worms in them

and 15 that have bruises. Only those apples with neither worms nor bruises can

be sold. If there are 10 bruised apples that have worms in them, how many of

the 100 apples can be sold?

In a mathematics contest with three problems, 80% of the participants solved

the first problem, 75% solved the second and 70% solved the third. Prove that

at least 25% of the participants solved all three problems.

How many positive integers less than 100 is not a factor of 2,3 and 5?

Two Balls are to be selected without replacement from a bag that contains one

red, one blue, one green and one orange ball. A) Use the counting principle to

determine the number of possible points in the sample space. Construct a tree

diagram and list the sample space.

In a survey on the gelato preferences of college students, the following data was

obtained: • 78 like mixed berry • 32 like irish cream • 57 like tiramisu • 13 like

both mixed berry and irish cream • 21 like both irish cream and tiramisu • 16

like both tiramisu and mixed berry • 5 like all three flavours above • 14 like none

of these three flavours How many students were surveyed?

There are 38 different time periods during which classes at a university can be

scheduled. If there are 677 different classes, how many different rooms will be

needed?

Show that in any set of six classes, each meeting regularly once a week on a

particular day of the week, there must be two that meet on the same day,

assuming that no classes are held on weekends.

Suppose 5 points are chosen at random in the interior of an equilateral triangle

T where each side has length two inches. Show that the distance between two of

the points must be less than one inch.

Consider a tournament with n players where each player plays against every

other player. Suppose each player wins at least once. Show that at least 2 of the

players have the same number of wins.

Find the minimum number n of integers to be selected from S = {1, 2, . . . , 9} so 

that: (a) The sum of two of the n integers is even. (b) The difference of two of the 

n integers is 5.