This is the Multiple Choice Questions Part 2 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 – 50**Answer key:

**PART I**

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

**PART II**

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

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

**Problem 51**

How permutation can be made out of the letters in the world island taking four letters at a time?

- A. 360
- B. 720
- C. 120
- D. 24

**Problem 52 (CE November 1996)**

How many 4 digit number can be formed without repeating any digit, from the following digit 1,2,3,4 and 6.

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

**Problem 53**

How many permutations can made out of the letters of the word ENGINEERING?

- A. 39,916,800
- B. 277,200
- C. 55,440
- D. 3,326,400

**Problem 54**

How many ways can 3 men and 4 women be seated on a bench if the women to be together?

- A. 720
- B. 576
- C. 5040
- D. 1024

**Problem 55**

In how many ways can 5 people line up to pay their electric bills?

- A. 120
- B. 1
- C. 72
- D. 24

**Problem 56**

In how many ways can 5 people line up to pay their electric bills, if two particular persons refuse to follow each other?

- A. 120
- B. 72
- C. 90
- D. 140

**Problem 57**

How many ways can 7 people be seated at a round table?

- A. 5040
- B. 120
- C. 720
- D. 840

**Problem 58**

In how many relative orders can we seat 7 people at a round table with a certain people side by side.

- A. 144
- B. 5040
- C. 720
- D. 1008

**Problem 59**

In how many ways can we seat 7 people in a round table with a certain 3 people not in consecutive order?

- A. 576
- B. 3960
- C. 5320
- D. 689

**Problem 60**

The captain of a baseball team assigns himself to the 4^{th} place in the batting order. In how many ways can he assign the remaining places to his eight teammates if just three men are eligible for the first position?

- A. 2160
- B. 40320
- C. 5040
- D. 15120

**Problem 61**

In how many ways can PICE 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. 630630
- B. 3300
- C. 5040
- D. 15120

**Problem 62**

How many ways can a committee of five be selected from an organization with 35 members?

- A. 324632
- B. 425632
- C. 125487
- D. 326597

**Problem 63**

How many line segments can be formed by 13 distinct point?

- A. 156
- B. 36
- C. 98
- D. 78

**Problem 64**

In how many ways can a hostess select six luncheon guests from 10 women if she is to avoid having particular two of them together at the luncheon?

- A. 210
- B. 84
- C. 140
- D. 168

**Problem 65 (ECE 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. 840
- C. 480
- D. 540

**Problem 66**

How many ways can you invite one or more of five friends to a party?

- A. 25
- B. 15
- C. 31
- D. 62

**Problem 67**

A bag contains 4 red balls, 3 green balls, and 5 blue balls. The probability of not getting a red ball in the first draw is:

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

**Problem 68**

Which of the following cannot be a probability?

- A. 1
- B. 0
- C. 1/e
- D. 0.434343

**Problem 69 (CE 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. 5/28
- B. 5/16
- C. 5/32
- D. 5/14

**Problem 70**

A bag contains 3 white and 5 red balls. If two balls are drawn at random, find the probability that both are white.

- A. 3/28
- B. 3/8
- C. 2/7
- D. 5/15

**Problem 71**

In problem 70, find the probability that one ball is white and the other is red.

- A. 15/56
- B. 15/28
- C. ¼
- D. 225/784

**Problem 72**

In the problem 70, find the probability that all are of the same color.

- A. 13/30
- B. 14/29
- C. 13/28
- D. 15/28

**Problem 73**

The probability that both stages of a two-stage rocket to function correctly is 0.92. The reliability of the first stage is 0.97. The reliability of the second stage is:

- A. 0.948
- B. 0.958
- C. 0.968
- D. 0.8924

**Problem 74**

Ricky and George each throw dice. If Ricky gets a sum of four what is the probability that George will get less than of four?

- A. ½
- B. 5/6
- C. 9/11
- D. 1/12

**Problem 75**

Two fair dice are thrown. What is the probability that the sum of the dice is divisible by 5?

- A. 7/36
- B. 1/9
- C. 1/12
- D. ¼

**Problem 76 (ME April 1996)**

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

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

**Problem 77**

If three balls in drawn in succession from 5 white and a second bag, find the probability that all are of one color, if the first ball is replaced immediately while the second is not replaced before the third draw.

- A. 10/121
- B. 18/121
- C. 28/121
- D. 180/14641

**Problem 78**

A first bag contains 5 white balls and 10 black balls. The experiment consists of selecting a bag and then drawing a ball from the selected bag. Find the probability of drawing a white ball.

- A. 1/3
- B. 1/6
- C. 1/2
- D. 1/8

**Problem 79**

In problem 78, find the probability of drawing a white ball from the first bag.

- A. 5/6
- B. 1/6
- C. 2/3
- D. 1/3

**Problem 80**

If seven coins are tossed simultaneously, find the probability that will just have three heads.

- A. 33/128
- B. 35/128
- C. 30/129
- D. 37/129

**Problem 81**

If seven coins are tossed simultaneously, find the probability that there will be at least six tails.

- A. 2/128
- B. 3/128
- C. 1/16
- D. 2/16

**Problem 82 (CE November 1998)**

A face of a coin is either head or tail. If three coins are tossed, what is are the probability of getting three tails?

- A. 1/8
- B. ½
- C. ¼
- D. 1/6

**Problem 83**

The face of a coin is either head or tail. If three coins are tossed, what is the probability of getting three tails or three heads?

- A. 1/8
- B. ½
- C. ¼
- D. 1/6

**Problem 84**

Five fair coins were tossed simultaneously. What is the probability of getting three heads and two tails?

- A. 1/32
- B. 1/16
- C. 1/8
- D. ¼

**Problem 85**

Throw a fair coin five times. What is the probability of getting three heads and two tails?

- A. 5/32
- B. 5/16
- C. 1/32
- D. 7/16

**Problem 86 (ECE March 1996)**

The probability of getting 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 87**

There are three short questions in mathematics test. For each question, one (1) mark will be awarded for a correct answer and no mark for a wrong answer. If the probability that Mary correctly answers a question in a test is 2/3, determine the probability that Mary gets two marks.

- A. 4/27
- B. 8/27
- C. 4/9
- D. 2/9

**Problem 88**

A marksman hits 75% of all his targets. What is the probability that he will hit exactly 4 of his next ten shot?

- A. 0.01622
- B. 0.4055
- C. 0.004055
- D. 0.001622

**Problem 89**

A two-digit number is chosen randomly. What is the probability that it is divisible by 7?

- A. 7/50
- B. 13/90
- C. 1/7
- D. 7/45

**Problem 90**

One box contains four cards numbered 1, 3,5,and 6. Another box contains three cards numbered 2, 4, and 7. One card is drawn from each bag. Find the probability that the sum is even.

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

**Problem 91**

Two people are chosen randomly from 4 married couples. What is probability that they are husband and wife?

- A. 1/28
- B. 1/14
- C. 3/28
- D. 1/7

**Problem 92**

One letter is taken from each of the words PARALLEL and LEVEL at random. What is the probability of getting the same letter?

- A. 1/5
- B. 1/20
- C. 3/20
- D. ¾

**Problem 93**

In a shooting game, the probability that Botoy and Toto will hit a target is 2/3 and ¾ respectively. What is the probability that the target is hit when both shoot at it once?

- A. 13/5
- B. 5/13
- C. 7/12
- D. 11/12

**Problem 94**

A standard deck of 52 playing cards is well shuffled. The probability that the first four cards dealt from the deck will be four aces is closes to:

- A. 4 x 10
^{-6} - B. 2 x 10
^{-6} - C. 3 x 10
^{-6} - D. 8 x 10
^{-6}

**Problem 95**

A card is chosen from pack of playing cards. What is the probability that it is either red or a picture card?

- A. 8/13
- B. 10/13
- C. 19/26
- D. 8/15

**Problem 96**

In a poker game consisting of 5 cards, what is the probability of holding 2 aces and 2 Queens?

- A. 5! /52!
- B. 5/52
- C. 33/54145
- D. 1264/45685

**Problem 97**

Dennis Rodman sinks 50% of all his attempts. What is the probability that he will make exactly 3 of his next 10 attempts?

- A. 1/256
- B. 3/8
- C. 30/128
- D. 15/128

**Problem 98**

There are 10 defectives per 1000 items of a product in long run. What is the probability that there is one and only one defective in random lot of 100?

- A. 0.3697
- B. 0.3967
- C. 0.3796
- D. 0.3679

**Problem 99**

The UN forces for Bosnia uses a type of missile that hits the target with a probability of 0.3. How many missiles should be fired so that there is at least an 80% probability of hitting the target?

- A. 2
- B. 4
- C. 5
- D. 3

**Problem 100 (ME April 1997)**

In a dice game, one fair is used. The player wins P20.00 if he rolls either 1 or 6. He losses P10.00 if he turns up any other face. What is the expected winning for one roll of the die?

- A. P40.00
- B. P0.00
- C. P20.00
- D. P10.00

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