Questions and Answers
How many permutations can be made out of the letters in the word ISLAND taking four letters at a time?
360
How many 4 digit numbers can be formed without repeating any digit, from the following digits 1, 2, 3, 4 and 6?
120
How many permutations can be made out of the letters of the word ENGINEERING?
277,200
How many ways can 3 men and 4 women be seated on a bench if the women are to be together?
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In how many ways can 5 people line up in any order?
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How many ways can 7 persons sit in a circular arrangement?
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How many ways can you invite one or more of five friends to a party?
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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:
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Which of the following cannot be a probability?
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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?
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A bag contains 3 white and 5 black balls. If two balls are drawn at random, what is the probability that both balls are white?
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In how many relative orders can we seat 7 people at a round table with a certain 3 people side by side?
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In how many ways can we seat 7 people in a round table with a certain 3 people not in consecutive order?
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The captain of a baseball team assigns himself to the 4th 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?
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How many ways can a committee of five be selected from an organization with 35 members?
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How many ways can a 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?
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How many line segments can be formed by 12 distinct points?
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When three coins are tossed, what is the probability of getting three tails?
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When three coins are tossed, what is the probability of getting three heads?
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If five fair coins are tossed simultaneously, what is the probability of getting three heads and two tails?
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When a fair coin is thrown five times, what is the probability of getting three heads and two tails?
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If the probability of getting a credit in an examination is 1/3, what is the probability that at least one out of three selected students got a credit?
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A 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 box. What is the probability that the sum is even?
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Two people are chosen randomly from 4 married couples. What is the probability that they are husband and wife?
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One letter is taken from each of the words PARALLEL and LEVEL at random. What is the probability of getting the same letter?
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A standard deck of 52 playing cards is well shuffled. What is the probability that the first four cards dealt from the deck will be the ten, ace, jack, and queen of spades?
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If one card is drawn randomly from a well-shuffled deck of 52 cards, what is the probability of drawing a spade?
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Ricky and George each throw two dice. If Ricky gets a sum of 4, what is the probability that George will get less?
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Two fair dice are thrown. What is the probability that the sum shown on the dice is divisible by 5?
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An urn contains 4 black balls and 6 white balls. What is the probability of getting one black ball and one white ball in two consecutive draws from the urn?
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If three balls are drawn in succession from 5 white and 6 black balls in a 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.
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A first bag contains 5 white balls and 11 black balls and a second bag contains 20 white balls and 10 black balls. The experiment consists of selecting one bag and then drawing a ball from the selected bag. Find the probability of drawing a white ball.
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If 3 red balls and 7 blue balls are typed randomly with numbers between 1 and 10, then the probability of drawing a red ball from a bag containing only 3 balls if the numbers are odd is:
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A fair coin is tossed three times. The probability of getting exactly two tails is:
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Ten tickets numbered 1 to 10 are put in a box. One ticket is drawn at random. Find the probability that the ticket drawn is a number greater than 3.
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What is the probability that Dennis Rodman will make exactly 3 of his next 10 attempts?
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There are 10 defectives per 1000 items of a product in the long run. What is the probability that there is one and only one defective in a random lot of 100?
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The UN forces for Bosnia use 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?
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In a dice game using one fair die, the player wins P2000.00 if they roll either a 1 or 6. They lose P1000.00 if any other face turns up. What is the expected winning for one roll of the die?
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Which type of distribution is used to determine the probability of exactly 3 successes in 10 trials for a process where each trial has a success rate of 50%?
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Study Notes
Permutation, Combination, and Probability
Permutations
- The number of permutations of the letters in the word ISLAND, taking four letters at a time, is 360.
- The number of permutations of the letters in the word ENGINEERING is 3,326,400.
- The number of ways to seat 7 people at a round table with a certain 3 people side by side is 144.
- The number of ways to seat 7 people in a round table with a certain 3 people not in consecutive order is 3960.
- The number of ways to seat 7 people in a round table is 5040.
Combinations
- The number of ways to choose a committee of five from an organization with 35 members is 324,632.
- The number of ways to select six luncheon guests from 12 women if a husband and a wife are to be together is 462.
- The number of line segments that can be formed by 12 distinct points is 66.
Probability
- The probability of not getting a red ball in the first draw from a bag containing 4 red balls, 3 green balls, and 5 blue balls is 2/3.
- The probability that both balls are black when two balls are drawn in succession without replacement from a bag containing 3 white and 5 black balls is 5/14.
- The probability that both balls are white when two balls are drawn at random from a bag containing 3 white and 5 black balls is 1/32.
- The probability that George will get less than Ricky when both throw two dice is 5/6.
- The probability that the sum shown on two thrown dice is divisible by 5 is 1/9.
- The probability of getting one black ball and one white ball in two consecutive draws from an urn containing 4 black balls and 6 white balls is 0.24.
- The probability of drawing a white ball from a bag containing 5 white balls and 11 black balls or a bag containing 20 white balls and 10 black balls is 173/351.
- The probability of drawing a red ball from a bag containing only 3 balls if the numbers are odd is 1/2.
- The probability of getting exactly two tails when a fair coin is tossed three times is 3/8.
- The probability of getting three tails when three coins are tossed is 1/8.
- The probability of getting three heads when three coins are tossed is 1/8.
- The probability of getting three heads and two tails when five fair coins are tossed simultaneously is 10/32.
- The probability of getting at least one credit in an examination, given that the probability of getting a credit is 1/3, is 19/27.
- The probability that the sum of two cards drawn from two boxes, one containing four cards numbered 1, 3, 5, and 6, and the other containing three cards numbered 2, 4, and 7, is even is 7/12.
- The probability that two people chosen randomly from 4 married couples are husband and wife is 1/14.
- The probability of getting the same letter when one letter is taken from each of the words PARALLEL and LEVEL at random is 3/16.
- The probability that the first four cards dealt from a standard deck of 52 playing cards will be the ten, ace, jack, and queen of spades is 1/(52 x 51 x 50 x 49).
- The probability that Dennis Rodman will make exactly 3 of his next 10 attempts, given that he sinks 50% of all his attempts, is 15/128.
- The probability that there is one and only one defective in a random lot of 100, given that there are 10 defectives per 1000 items of a product in a long run, is 0.3697.
- The number of missiles that should be fired so that there is at least an 80% probability of hitting the target, given that the probability of hitting the target with one missile is 0.3, is at least 4.
- The expected winning for one roll of the die in a dice game, given that the player wins P2000.00 if he rolls either 1 or 6 and loses P1000.00 if he turns up any other face, is P1000.00.
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Description
This set of problems from Engineering Mathematics Vol 1 covers permutation, combination, and probability concepts. Students can practice and test their knowledge with these exercises.
