Discrete Mathematics Answers

There are four roads from city X to Y and five roads from city Y to Z, find

(i) how many ways is it possible to travel from city X to city Z via city Y.

(ii) how different round trip routes are there from city X to Y to Z to Y and back

to X.

Teams A and B play in a tournament. The first team to win three games wins the

tournament. Find the number n of possible ways the tournament can occur.

Mark and Erik are to play a tennis tournament. The first person to win two

games in a row or who wins a total of three games wins the tournament. Find

the number of ways the tournament can occur.

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.

Let A, B, C, D denote, respectively, art, biology, chemistry, and drama courses.

Find the number N of students in a dormitory given the data:

12 take A, 5 takeAand B, 4 takeB and D, 2 take B, C,D,

20 take B, 7 takeAand C, 3 takeC and D, 3 take A, C,D,

20 take C, 4 takeAand D, 3 take A, B,C, 2 take all four,

8 take D, 16 takeB and C, 2 take A, B, D, 71 take none.

Suppose among 32 people who save paper or bottles (or both) for recycling,

there are 30 who save paper and 14 who save bottles. Find the number m of

people who:

(a) save both; (b) save only paper; (c) save only bottles.

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.