Math Reviewer

Solve each of the following problems.
1. There are 4 trails that lead to a camp on a hill. In how many ways can a camper go up
and down the hill by
a. any trail?
b. going up by one trail and going down by a different trail?
2. In a five-item true or false quiz, a student decided to write at random true or false.
In how many ways can he answer the quiz?
3. In how many different ways can you arrange 5 different books in a shelf?
4. A building has 5 entrance doors and 3 exit doors. In how many ways can a person
enter and leave the building?
5. There are 5 universities in a city. In how many ways can three Grade 12 students
enroll in these universities if no two of them may go to the same university?
6. In how many ways can a pair of fair dice fall when rolled?
7. In how many ways can 3 tossed coins fall?
8. How many three-letter codes can be formed from the letters L, O, V, E if the first letter
and the last letter must be a vowel?
9. How many numbers between 1 and 199 inclusive do not have the digit 3?
10. How many four-digit numbers can be formed from the digits 0, 1, 2, ..., 9 if
a. repetition of digits is allowed?
b. repetition of digits is not allowed?
c. the numbers formed are less than 5000?
d. the numbers formed are at least 5000?
e. the numbers are even?
1. An art gallery has acquired 12 paintings for exhibit. However, the gallery does not
have enough wall space to display all the paintings and can only accommodate 5.
How many possible ways are there to display the paintings?
2. In how many ways can 6 students be arranged in a line for picture taking?
3. In how many ways can 3 boys and 3 girls be seated in a row of 6 chairs if
a. they may sit anywhere?
b. the boys and girls must alternate?
c. all the girls must sit side by side and all the boys must do the same?
4. Seven chairs from 10 available chairs are to be arranged in a row for a meeting.
In how many ways can this be done if a specific chair is placed in the center for the
chairman?
5. How many different ordered arrangements can be made with 2 red, 2 white, and
3 blue balls?
6. In how many ways can you arrange all the letters

a. ARRANGEMENT?
b. BOOKKEEPER?
c. COMMITTEE?
d. CURRICULUM?
e. INTERFERENCE?
7. In how many ways can 5 books be arranged in a shelf if

a. the books may be arranged in any way?
b. two particular books must not be together?
8. In how many ways can 10 children form a circle?
9. In how many ways can 5 people sit at a round table if

a. two insist on sitting next to each other?
b. two refuse to sit next to each other?
10.In how many ways can 6 boys and 6 girls sit at a round table if
a. the boys and girls must alternate?
b. all the girls must sit next to each other and the boys sit in any way?
c. all the girls must sit next to each other and all the boys must do the same?
1. In how many ways can a committee of 4 be selected from a group of 12 persons?
2. In how many ways can a set of 5 cards be chosen from a standard deck of 52 cards?
3. There are 7 distinct points on a circle. How many inscribed triangles can be drawn
using the 7 points as vertices?
4. How many lines are determined by 6 points, no three of which are collinear?
5. How many diagonals does an octagon have?
6. In how many ways can 2 consonants and 1 vowel be chosen out of the letters of
ARNOLD?
7. A school has to send a delegation to a youth forum. In how many ways can a
delegation of at least 3 and at most 6 students to be formed from 10 students?
8. Mrs. Soliaban has 4 close friends. In how many ways can she invite at most 3 of
them to her wedding anniversary party?
9. A team of 5 is to be chosen from 6 boys and 3 girls. In how many ways can this be
done if the team must contain
a. exactly 2 boys?
b. exactly 2 girls?
c. at least 3 boys and at most 2 girls?
10.Given a deck of 52 playing cards, in how many ways can a hand with
a. three red and 2 black cards dealt?
b. all black cards be dealt?
c. one ace and 4 red cards be dealt?
obtained?
2. A group of 12 people needs to ride in two vehicles. If one vehicle can accommodate 7
people while the other can accommodate 5 people, in how many ways can the group be
divided for a ride?
3. In how many ways can two boys and 2 girls be arranged in a line for picture taking?
4. How many different 10-digit numbers can be made from the digits 1, 1, 2, 2, 2, 5, 5, 5, 7,
7 all together in all possible ways?
5. In how many ways can 10 identical beads of 5 different colors (2 red, 2 blue, 2 yellow,
2 green, and 2 white) be used to form a necklace if beads of the same color follow each
other?
6. In how many ways can a set of 3 math books and 2 science books be selected from a set
of 6 different math books and 5 different science books?
7. In how many ways can 4 boys and 3 girls be seated in a row of 7 chairs if boy and girls
must alternate?
8. A box contains 3 red balls, 2 white balls, and 1 blue ball. In how many ways can 4 balls
be chosen if exactly 2 balls must be red?
9. In how many ways can the letters A, B, C, D, E, F, G, and H be arranged so that A and B
are next to each other?
10. From 6 men and 2 women, a committee of 3 is formed. In how many ways can this be
done if a committee is to have exactly 2 men?

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Solve each of the following problems.

7. In how many ways can 3 tossed coins fall?

b. repetition of digits is not allowed?

c. the numbers formed are less than 5000?

d. the numbers formed are at least 5000?

e. the numbers are even?

6. In how many ways can you arrange all the letters

7. In how many ways can 5 books be arranged in a shelf if

8. In how many ways can 10 children form a circle?

9. In how many ways can 5 people sit at a round table if

1. In how many ways can a committee of 4 be selected from a group of 12 persons?

5. How many diagonals does an octagon have?

c. at least 3 boys and at most 2 girls?

b. all black cards be dealt?

c. one ace and 4 red cards be dealt?

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