This is the Multiple Choice Questions Part 1 of the Series in Venn Diagram, Permutation, Combination and Probability topics in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

### Multiple Choice Questions Topic Outline

- MCQs in Venn Diagram | MCQs in Fundamental Principle of Counting | MCQs in Permutation | MCQs in Combination | MCQs in Probability | MCQs in Conditional Probability | MCQs in Binomial or Repeated Probability

### Online Questions and Answers in Venn Diagram, Permutation, Combination and Probability Series

Following is the list of multiple choice questions in this brand new series:

**Venn Diagram, Permutation, Combination and Probability MCQs**

**MCQs from Number 1 โ 50**Answer key:

**PART I**

**MCQs from Number 51 โ 100**Answer key:

**PART II**

### Start Practice Exam Test Questions Part I of the Series

**Choose the letter of the best answer in each questions.**

**Problem 1: EE Board October 1993**

In a class 40 students, 27 like Calculus and 25 like Chemistry. How many like both **Calculus and Chemistry**?

- A. 10
- B. 11
- C. 12
- D. 13

**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?

- A. 10
- B. 11
- C. 12
- D. 13

**Problem 3: GE Board February 1994**

A survey of 100 persons revealed that 72 of them had eaten at restaurant P and that 52 of them had eaten at restaurant Q. Which of the following could not be the number of persons in the surveyed group who had eaten at both P and Q?

- A. 20
- B. 22
- C. 24
- D. 26

**Problem 4: ECE Board November 1992**

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 subjects, find the number of examinees from that school who took the examinations.

- A. 20
- B. 25
- C. 30
- D. 28

**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 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 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. 280
- B. 230
- C. 180
- D. 130

**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. The following statistics were found: 6 people used all three brands, 5 used only Hapee and Close-up, 18 used 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?

- A. Neither yes nor no
- B. Yes
- C. No
- D. Either yes or no

**Problem 7:**

How many four-letter words beginning and ending with a vowel without any letter repeated can be formed from the word โpersonnelโ?

- A. 40
- B. 480
- C. 20
- D. 312

**Problem 8:**

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. 292
- B. 5760
- C. 34560
- D. 12870

**Problem 9:**

The number of ways can 3 nurses and 4 engineers be seated on a bench with the nurses seated together is?

- A. 144
- B. 258
- C. 720
- D. 450

**Problem 10: ECE Board November 1998**

If 15 people won prizes in the state lottery (assuming that there are no ties), how many ways can these 15 people win first, second, third, fourth and fifth prizes?

- A. 4,845
- B. 116,260
- C. 360,360
- D. 3,003

**Problem 11: CE Board November 1996**

How many 4 digit numbers can be formed without repeating any digit from the following digits: 1, 2, 3, 4 and 6?

- A. 120
- B. 130
- C. 140
- D. 150

**Problem 12: EE Board June 1990**

How many permutations are there if the letters PNRCSE are taken six at a time?

- A. 1440
- B. 480
- C. 720
- D. 360

**Problem 13: EE Board April 1996**

In how many ways can 6 distinct books be arranged in a bookshelf?

- A. 720
- B. 120
- C. 360
- D. 180

**Problem 14: EE Board April 1997**

What is the number of permutations of the letters in the word BANANA?

- A. 36
- B. 60
- C. 52
- D. 42

**Problem 15: ME Board April 1994**

A PSME unit has 10 MEโs, 8 PMEโs and 6 CPMโs. If a committee of 3 members, one from each group is to be formed, how many such committees can be formed?

- A. 2,024
- B. 12,144
- C. 480
- D. 360

**Problem 16: ME Board October 1992**

In how many ways can a PSME Chapter with 15 directors choose a President, a Vice President, a Secretary, a Treasurer and an Auditor, if no member can hold more than one position?

- A. 360,360
- B. 32,760
- C. 3,003
- D. 3,603,600

**Problem 17: EE Board October 1997**

Four different colored flags can be hung in a row to make coded signal. How many signals can be made if a signal consists of the display of one or more flags?

- A. 64
- B. 66
- C. 68
- D. 62

**Problem 18: EE Board June 1990, EE Board April 1993, CHE Board May 1994**

In how many ways can 4 boys and 4 girls be seated alternately in a row of 8 seats?

- A. 1152
- B. 2304
- C. 576
- D. 2204

**Problem 19: EE Board October 1997**

There are four balls of four different colors. Two balls are taken at a time and arranged in a definite order. For example, if a white and red balls are taken, one definite arrangement is white first, red second, and another arrangement is red first, white second. How many such arrangements are possible?

- A. 24
- B. 6
- C. 12
- D. 36

**Problem 20:**

How many different ways can 5 boys and 5 girls form a circle with boys and girls alternate?

- A. 28,800
- B. 2,880
- C. 5,600
- D. 14,400

**Problem 21: EE Board October 1997**

There are four balls of different colors. Two balls at a time are taken and arranged any way. How many such combinations are possible?

- A. 36
- B. 3
- C. 6
- D. 12

**Problem 22: EE Board March 1998**

How many 6-number combinations can be generated from the numbers from 1 to 42 inclusive, without repetition and with no regards to the order of the numbers?

- A. 850,668
- B. 5,245,786
- C. 188,848,296
- D. 31,474,716

**Problem 23:**

Find the total number of combinations of three letters, J, R, T taken 1, 2, 3 at a time.

- A. 7
- B. 8
- C. 9
- D. 10

**Problem 24: ME Board October 1997**

In how many ways can you invite one or more of your five friends in a party?

- A. 15
- B. 31
- C. 36
- D. 25

**Problem 25: CHE November 1996**

In how many ways can a committee of three consisting of two chemical engineers and one mechanical engineer can be formed from four chemical engineers and three mechanical engineers?

- A. 18
- B. 64
- C. 32
- D. None of these

**Problem 26: EE Board April 1995**

In Mathematics examination, a student may select 7 problems from a set of 10 problems. In how many ways can he make his choice?

- A. 120
- B. 530
- C. 720
- D. 320

**Problem 27: EE Board April 1997**

How many committees can be formed by choosing 4 men from an organization of a membership of 15 men?

- A. 1390
- B. 1240
- C. 1435
- D. 1365

**Problem 28: ECE Board April 1998**

A semiconductor company will hire 7 men and 4 women. In how many ways can the company choose from 9 men and 6 women who qualified for the position?

- A. 680
- B. 540
- C. 480
- D. 840

**Problem 29: ECE Board April 1994**

There are 13 teams in a tournament. Each team is to play with each other only once. What is the minimum number of days can they all play without any team playing more than one game in any day?

- A. 11
- B. 12
- C. 13
- D. 14

**Problem 30: EE Board October 1996**

There are five main roads between the cities A and B, and four between B and C. In how many ways can a person drive from A to C and return, going through B on both trips without driving on the same road twice?

- A. 260
- B. 240
- C. 120
- D. 160

**Problem 31: EE Board April 1991**

There are 50 tickets in a lottery in which there is a first and second prize. What is the probability of a man drawing a prize if he owns 5 tickets?

- A. 50%
- B. 25%
- C. 20%
- D. 40%

**Problem 32:**

Roll a pair of dice. What is the probability that the sum of two numbers is 11?

- A. 1/36
- B. 1/9
- C. 1/18
- D. 1/20

**Problem 33:**

Roll two dice once. What is the probability that the sum is 7?

- A. 1/6
- B. 1/8
- C. 1/4
- D. 1/7

**Problem 34:**

In a throw of two dice, the probability of obtaining a total of 10 or 12 is?

- A. 1/6
- B. 1/9
- C. 1/12
- D. 1/18

**Problem 35:**

Determine the probability of drawing either a king or a diamond in a single draw from a pack of 52 playing cards

- A. 2/13
- B. 3/13
- C. 4/13
- D. 1/13

**Problem 36:**

A card is drawn from a deck of 52 playing cards, Find the probability if drawing a king or a red card.

- A. 0.5835
- B. 0.5385
- C. 0.3585
- D. 0.8535

**Problem 37: CE Board November 1998**

A coin is tossed 3 times. What is the probability of getting 3 tails up?

- A. 1/8
- B. 1/16
- C. 1/4
- D. 7/8

**Problem 38: EE Board April 1996**

The probability of getting at least 2 heads when a coin is tossed four times is?

- A. 11/16
- B. 13/16
- C. 1/4
- D. 3/8

**Problem 39:**

A fair coin is tossed three times. What is the probability of getting either 3 heads or 3 tail?

- A. 1/8
- B. 3/8
- C. 1/4
- D. 1/2

**Problem 40: ECE Board March 1996**

The probability of getting a credit in an examination is 1/3. If three students are selected at random, what is the probability that at least one of them got a credit?

- A. 19/27
- B. 8/27
- C. 2/3
- D. 1/3

**Problem 41:**

There are 3 questions in a test. For each question is awarded for a correct answer and none for a wrong answer. If the probability that Janine correctly answers a question in the test is 2/3, determine the probability that she gets zero in the test.

- A. 8/27
- B. 4/9
- C. 1/30
- D. 1/27

**Problem 42: EE Board April 1991**

In the ECE Board Examinations, the probability that an examinee will pass each subject is 0.8. What is the probability that an examinee will pass at least two subjects out of three board subjects?

- A. 70.9%
- B. 80.9%
- C. 85.9%
- D. 89.6%

**Problem 43:**

In a multiple choice test, each question is to be answered by selecting 1 out of 5 choices of which only 1 is right, If there are 10 questions in a test, what is the probability of getting 6 right of pure guesswork?

- A. 10%
- B. 6%
- C. 0.44%
- D. 0.55%

**Problem 44: ME Board April 1994**

From a box containing 6 red balls, 8 white balls and 10 blue balls, one ball is drawn at random. Determine the probability that is red or white.

- A. 1/3
- B. 7/12
- C. 5/12
- D. 1/4

**Problem 45: EE Board October 1990**

From a bag containing 4 black balls and 5 white balls, two balls are drawn one at a time. Find the probability that both balls are white. Assume that the first ball is returned before the second ball is drawn.

- A. 25/81
- B. 16/81
- C. 5/18
- D. 40/81

**Problem 46: CE Board May 1996**

A bag contains 3 white and 5 black balls. If two balls are drawn in succession without replacement, what is the probability that both balls are black?

- A. 5/16
- B. 5/28
- C. 5/32
- D. 5/14

**Problem 47: ME Board April 1996**

An urn contains 4 black balls and 6 white balls. What is the probability of getting 1 black and 1 white ball in two consecutive draws from the urn?

- A. 0.24
- B. 0.27
- C. 0.53
- D. 0.04

**Problem 48: EE Board October 1990**

From a bag containing 4 black balls and 5 white balls, two balls are drawn one at a time. Find the probability that one ball is white and one ball is black. Assume that the first ball is returned before the second ball is drawn.

- A. 16/81
- B. 25/81
- C. 20/81
- D. 40/81

**Problem 49: EE Board October 1997**

A group of 3 people enter a theatre after the lights had dimmed. They are shown to the correct group of 3 seats by the usher. Each person holds a number stub. What is the probability that each is in the correct seat according to the numbers on seat and stub?

- A. 1/6
- B. 1/4
- C. 1/2
- D. 1/8

**Problem 50:**

From 20 tickets marked with the first 20 numerals, one is drawn at random. What is the chance that it will be a multiple of 3 or of 7?

- A. 1/2
- B. 8/15
- C. 3/10
- D. 2/5

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