Choose the letter of the best answer in each questions. Problem 5: EE Board April 1997
In a commercial survey involving 1000 persons on brand preference, 120 were found to prefer brand x only, 200
Problem 1: EE Board October 1993 prefer brand y only, 150 prefer brand z only, 370 prefer either brand x or y but not z, 450 prefer brand y or z but not
In a class 40 students, 27 like Calculus and 25 like Chemistry. How many like both Calculus and Chemistry? x and 370 prefer either brand z or x but not y. How many persons have no brand preference, satisfied with any of
the three brands?
A. 10
B. 11 A. 280
C. 12 B. 230
D. 13 C. 180
D. 130
Problem 2: ECE Board November 1998
A club of 40 executives, 33 like to smoke Marlboro and 20 like to smoke Philip Morris. How many like both? Problem 6: EE Board April 1997
A toothpaste firm claims that in survey of 54 people, they were using either Colgate, Hapee or Close-up brand.
A. 10 The following statistics were found: 6 people used all three brands, 5 used only Hapee and Close-up, 18 used
B. 11 Hapee or Close-up, 2 used Hapee, 2 used only Hapee and Colgate, 1 used Close-up and Colgate, and 20 used
only Colgate. Is the survey worth paying for?
C. 12
D. 13
A. Neither yes nor no
Problem 3: GE Board February 1994 B. Yes
A survey of 100 persons revealed that 72 of them had eaten at restaurant P and that 52 of them had eaten at C. No
restaurant Q. Which of the following could not be the number of persons in the surveyed group who had eaten at D. Either yes or no
both P and Q?
Problem 7:
A. 20 How many four-letter words beginning and ending with a vowel without any letter repeated can be formed from the
word “personnel”?
B. 22
C. 24
A. 40
D. 26
B. 480
C. 20
Problem 4: ECE Board November 1992 D. 312
The probability for the ECE board examinees from a certain school to pass the subject Mathematics is 3/7 and for the
subject Communications is 5/7. If none of the examinees fails both subject and there are 4 examinees who pass both Problem 8:
subjects, find the number of examinees from that school who took the examinations. Five different Mathematics books, 4 different electronics books and 2 different communications books are to be
placed in a shelf with the books of the same subject together. Find the number of ways in which the books can be
placed.
A. 20
B. 25
A. 292
C. 30
B. 5760
D. 28
C. 34560
D. 12870
, Problem 9: Problem 14: EE Board April 1997
The number of ways can 3 nurses and 4 engineers be seated on a bench with the nurses seated together is? What is the number of permutations of the letters in the word BANANA?
A. 36
A. 144
B. 60
B. 258
C. 52
C. 720
D. 42
D. 450
Problem 15: ME Board April 1994
Problem 10: ECE Board November 1998 A PSME unit has 10 ME’s, 8 PME’s and 6 CPM’s. If a committee of 3 members, one from each group is to be
If 15 people won prizes in the state lottery (assuming that there are no ties), how many ways can these 15 people win formed, how many such committees can be formed?
first, second, third, fourth and fifth prizes?
A. 2,024
A. 4,845
B. 12,144
B. 116,260
C. 480
C. 360,360
D. 360
D. 3,003
Problem 16: ME Board October 1992
Problem 11: CE Board November 1996 In how many ways can a PSME Chapter with 15 directors choose a President, a Vice
How many 4 digit numbers can be formed without repeating any digit from the following digits: 1, 2, 3, 4 and 6?
President, a Secretary, a Treasurer and an Auditor, if no member can hold more than one position?
A. 120
A. 360,360
B. 130
B. 32,760
C. 140
C. 3,003
D. 150
D. 3,603,600
Problem 12: EE Board June 1990
Problem 17: EE Board October 1997
How many permutations are there if the letters PNRCSE are taken six at a time?
Four different colored flags can be hung in a row to make coded signal. How many signals can be made if a signal
A. 1440 consists of the display of one or more flags?
B. 480
A. 64
C. 720
B. 66
D. 360
C. 68
Problem 13: EE Board April 1996 D. 62
In how many ways can 6 distinct books be arranged in a bookshelf?
Problem 18: EE Board June 1990, EE Board April 1993, CHE Board May 1994
A. 720 In how many ways can 4 boys and 4 girls be seated alternately in a row of 8 seats?
B. 120
C. 360 A. 1152
D. 180 B. 2304
C. 576
D. 2204
In a commercial survey involving 1000 persons on brand preference, 120 were found to prefer brand x only, 200
Problem 1: EE Board October 1993 prefer brand y only, 150 prefer brand z only, 370 prefer either brand x or y but not z, 450 prefer brand y or z but not
In a class 40 students, 27 like Calculus and 25 like Chemistry. How many like both Calculus and Chemistry? x and 370 prefer either brand z or x but not y. How many persons have no brand preference, satisfied with any of
the three brands?
A. 10
B. 11 A. 280
C. 12 B. 230
D. 13 C. 180
D. 130
Problem 2: ECE Board November 1998
A club of 40 executives, 33 like to smoke Marlboro and 20 like to smoke Philip Morris. How many like both? Problem 6: EE Board April 1997
A toothpaste firm claims that in survey of 54 people, they were using either Colgate, Hapee or Close-up brand.
A. 10 The following statistics were found: 6 people used all three brands, 5 used only Hapee and Close-up, 18 used
B. 11 Hapee or Close-up, 2 used Hapee, 2 used only Hapee and Colgate, 1 used Close-up and Colgate, and 20 used
only Colgate. Is the survey worth paying for?
C. 12
D. 13
A. Neither yes nor no
Problem 3: GE Board February 1994 B. Yes
A survey of 100 persons revealed that 72 of them had eaten at restaurant P and that 52 of them had eaten at C. No
restaurant Q. Which of the following could not be the number of persons in the surveyed group who had eaten at D. Either yes or no
both P and Q?
Problem 7:
A. 20 How many four-letter words beginning and ending with a vowel without any letter repeated can be formed from the
word “personnel”?
B. 22
C. 24
A. 40
D. 26
B. 480
C. 20
Problem 4: ECE Board November 1992 D. 312
The probability for the ECE board examinees from a certain school to pass the subject Mathematics is 3/7 and for the
subject Communications is 5/7. If none of the examinees fails both subject and there are 4 examinees who pass both Problem 8:
subjects, find the number of examinees from that school who took the examinations. Five different Mathematics books, 4 different electronics books and 2 different communications books are to be
placed in a shelf with the books of the same subject together. Find the number of ways in which the books can be
placed.
A. 20
B. 25
A. 292
C. 30
B. 5760
D. 28
C. 34560
D. 12870
, Problem 9: Problem 14: EE Board April 1997
The number of ways can 3 nurses and 4 engineers be seated on a bench with the nurses seated together is? What is the number of permutations of the letters in the word BANANA?
A. 36
A. 144
B. 60
B. 258
C. 52
C. 720
D. 42
D. 450
Problem 15: ME Board April 1994
Problem 10: ECE Board November 1998 A PSME unit has 10 ME’s, 8 PME’s and 6 CPM’s. If a committee of 3 members, one from each group is to be
If 15 people won prizes in the state lottery (assuming that there are no ties), how many ways can these 15 people win formed, how many such committees can be formed?
first, second, third, fourth and fifth prizes?
A. 2,024
A. 4,845
B. 12,144
B. 116,260
C. 480
C. 360,360
D. 360
D. 3,003
Problem 16: ME Board October 1992
Problem 11: CE Board November 1996 In how many ways can a PSME Chapter with 15 directors choose a President, a Vice
How many 4 digit numbers can be formed without repeating any digit from the following digits: 1, 2, 3, 4 and 6?
President, a Secretary, a Treasurer and an Auditor, if no member can hold more than one position?
A. 120
A. 360,360
B. 130
B. 32,760
C. 140
C. 3,003
D. 150
D. 3,603,600
Problem 12: EE Board June 1990
Problem 17: EE Board October 1997
How many permutations are there if the letters PNRCSE are taken six at a time?
Four different colored flags can be hung in a row to make coded signal. How many signals can be made if a signal
A. 1440 consists of the display of one or more flags?
B. 480
A. 64
C. 720
B. 66
D. 360
C. 68
Problem 13: EE Board April 1996 D. 62
In how many ways can 6 distinct books be arranged in a bookshelf?
Problem 18: EE Board June 1990, EE Board April 1993, CHE Board May 1994
A. 720 In how many ways can 4 boys and 4 girls be seated alternately in a row of 8 seats?
B. 120
C. 360 A. 1152
D. 180 B. 2304
C. 576
D. 2204
