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23. How many even three digit numbers greater than 400 can be formed from 1, 2, 3, 4, 5, 6, 7, 8, and 9 if no digit is to be repeated? 24. Suppose you find seven articles related to your research paper. In how many ways can you choose five articles to read? 25. Jack is visiting a small country in Europe. There are 8 attractions for sightseeing and he can visit these places in any order. Due to lack of time, Jack can only visit 5 places. Suppose Jack must visit the national park, how many possible sequences are there? 26. A factory produces light bulbs on 2 production lines, A and B. the manager selects 3 out of the first 8 light bulbs from line A and 5 out of the first 11 light bulbs from line B for a quality test. After selecting the light bulbs, the manager will test the light bulbs one by one. If the light bulbs from line B must be tested first, how many different arrangements are there? 27. Four letters are selected from the word DISPLAY, Find the number of combinations that include exactly two letters from the word PLAY. 28. A pair of dice is thrown. What is the probability that one will roll an even number? 29. Two dice are thrown What is the probability that one will roll a sum of 9?

23. How many even three digit numbers greater than 400 can be formed from 1, 2, 3, 4, 5, 6, 7, 8, and 9 if no digit is to be repeated? 24. Suppose you find seven articles related to your research paper. In how many ways can you choose five articles to read? 25. Jack is visiting a small country in Europe. There are 8 attractions for sightseeing and he can visit these places in any order. Due to lack of time, Jack can only visit 5 places. Suppose Jack must visit the national park, how many possible sequences are there? 26. A factory produces light bulbs on 2 production lines, A and B. the manager selects 3 out of the first 8 light bulbs from line A and 5 out of the first 11 light bulbs from line B for a quality test. After selecting the light bulbs, the manager will test the light bulbs one by one. If the light bulbs from line B must be tested first, how many different arrangements are there? 27. Four letters are selected from the word DISPLAY, Find the number of combinations that include exactly two letters from the word PLAY. 28. A pair of dice is thrown. What is the probability that one will roll an even number? 29. Two dice are thrown What is the probability that one will roll a sum of 9?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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23. How many even three digit numbers greater than 400 can be formed from 1, 2, 3, 4, 5, 6, 7, 8, and 9 if no digit is to be repeated? 24. Suppose you find seven articles related to your research paper. In how many ways can you choose five articles to read? 25. Jack is visiting a small country in Europe. There are 8 attractions for sightseeing and he can visit these places in any order. Due to lack of time, Jack can only visit 5 places. Suppose Jack must visit the national park, how many possible sequences are there? 20. A factory produces light bulbs on 2 production lines, A and B. the manager selects 3 out of the first 8 light bulbs from line A and 5 out of the first 11 light bulbs from line B for a quality test. After selecting the light bulbs, the manager will test the light bulbs one by one. If the light bulbs from line B must be tested first, how many different arrangements are there? 27. Four letters are selected from the word DISPLAY, Find the number of combinations that include exactly two letters from the word PLAY. 28. A pair of dice is thrown. What is the probability that one will roll an even number? 29. Two dice are thrown, What is the probability that one will roll a sum of 97 30. Two dice are thrown, What is the probability that one will roll an odd and an even? 31. Mike tosses 11 coins. What is the probability that he will get at least 3 tails? 32. Mike tosses 11 coins, What is the probability that he will get 9 heads and 2 tails? S5. There are 10 contestants each in an oratorical and declamation contest representing 10 different schools. What is the probability that the winner in each of the two contests come from the same school? 34. A pair of dice is thrown. What is the probability of rolling a sum greater than 7? 35. A card is drawn from a standard deck of 52 cards, What is the probability that the card drawn is neither a diamond nor a spade? 50. Seven seats are put in a row from left to right, If four people take a seat at random, find the probability that those four people sit at the end of the row. 37. Peter has two kinds of snacks: potato chips of 3 different kinds and biscuits of 4 different kinds. He selects 3 packs of snack at random. Find the probability that the snacks are of the same kind. 38. Three cards are selected at random from a pack of 52 playing cards. Find the probability that there are 2 face cards and an ace. 39. The History club at a school consists of 10 members including John. 4 students are selected at random to visit a new museum. Find the probability that the letters T, R, and Y are put together. 40. The letter of the word CHEMISTRY are arranged in a row randomly. Find the probability that the letters T, R, and Y are put together. 41. Two letters are chosen from the word COLLOCATION one by one with replacement. Find the probability that neither of them is vowel. 42. A card is drawn at random from a deck of 52 playing cards. Find the probability that a 'Heart' or a 'Queen' is drawn. 43. Of the 30 members of a music club, 12 can play guitar, 15 can play piano but none of them can play both instruments. Find the probability that a member selected at random can play guitar or a piano. 44. Jane has 4 gold rings, 6 diamond rings, and 2 silver rings. If she choose one of the rings at random, find the probability that the chosen ring is either a gold or a diamond ring. 45. A bag contains 8 yellow balls that are marked with numbers 1 to 8 and 4 balls that are marked with numbers 1 to 4. A ball is chosen at random from the bag. Find the probability that it is a blue ball given that the number is odd. 46. Two letters are selected at random one by one from the word DIPLOMA without replacement. Find the probability that both letters are vowel. 47. A box contains 8 cups of which 5 are red and 3 are blue. Two cups are taken out at random one by one without replacement. Find the probability that the cups are of different colors. 48. Mary received a box of chocolate bars which contains 8 chocolate bars with nuts. Mary takes out one bar at random. Then, she takes out another bar at random. Find the probability that Mary takes 2 chocolate bars with nuts. 49. There are 8 cards in an envelope numbered 1,3, 5, 7, 9, 11, 13 and 15. John takes two cards one by one without replacement. Find the probability that both cards are marked with prime numbers. 50. John has 5 shirts of which 2 are white and 3 are blue. He also has 6 ties of which 3 are yellow and 3 are blue. He also has 6 ties of which 3 are yellow and 3 are blue. One morning, John selects a shirt and a tie at random. Find the probability that he has chosen a white shirt and a yellow tie.
Transcribed Image Text:23. How many even three digit numbers greater than 400 can be formed from 1, 2, 3, 4, 5, 6, 7, 8, and 9 if no digit is to be repeated? 24. Suppose you find seven articles related to your research paper. In how many ways can you choose five articles to read? 25. Jack is visiting a small country in Europe. There are 8 attractions for sightseeing and he can visit these places in any order. Due to lack of time, Jack can only visit 5 places. Suppose Jack must visit the national park, how many possible sequences are there? 20. A factory produces light bulbs on 2 production lines, A and B. the manager selects 3 out of the first 8 light bulbs from line A and 5 out of the first 11 light bulbs from line B for a quality test. After selecting the light bulbs, the manager will test the light bulbs one by one. If the light bulbs from line B must be tested first, how many different arrangements are there? 27. Four letters are selected from the word DISPLAY, Find the number of combinations that include exactly two letters from the word PLAY. 28. A pair of dice is thrown. What is the probability that one will roll an even number? 29. Two dice are thrown, What is the probability that one will roll a sum of 97 30. Two dice are thrown, What is the probability that one will roll an odd and an even? 31. Mike tosses 11 coins. What is the probability that he will get at least 3 tails? 32. Mike tosses 11 coins, What is the probability that he will get 9 heads and 2 tails? S5. There are 10 contestants each in an oratorical and declamation contest representing 10 different schools. What is the probability that the winner in each of the two contests come from the same school? 34. A pair of dice is thrown. What is the probability of rolling a sum greater than 7? 35. A card is drawn from a standard deck of 52 cards, What is the probability that the card drawn is neither a diamond nor a spade? 50. Seven seats are put in a row from left to right, If four people take a seat at random, find the probability that those four people sit at the end of the row. 37. Peter has two kinds of snacks: potato chips of 3 different kinds and biscuits of 4 different kinds. He selects 3 packs of snack at random. Find the probability that the snacks are of the same kind. 38. Three cards are selected at random from a pack of 52 playing cards. Find the probability that there are 2 face cards and an ace. 39. The History club at a school consists of 10 members including John. 4 students are selected at random to visit a new museum. Find the probability that the letters T, R, and Y are put together. 40. The letter of the word CHEMISTRY are arranged in a row randomly. Find the probability that the letters T, R, and Y are put together. 41. Two letters are chosen from the word COLLOCATION one by one with replacement. Find the probability that neither of them is vowel. 42. A card is drawn at random from a deck of 52 playing cards. Find the probability that a 'Heart' or a 'Queen' is drawn. 43. Of the 30 members of a music club, 12 can play guitar, 15 can play piano but none of them can play both instruments. Find the probability that a member selected at random can play guitar or a piano. 44. Jane has 4 gold rings, 6 diamond rings, and 2 silver rings. If she choose one of the rings at random, find the probability that the chosen ring is either a gold or a diamond ring. 45. A bag contains 8 yellow balls that are marked with numbers 1 to 8 and 4 balls that are marked with numbers 1 to 4. A ball is chosen at random from the bag. Find the probability that it is a blue ball given that the number is odd. 46. Two letters are selected at random one by one from the word DIPLOMA without replacement. Find the probability that both letters are vowel. 47. A box contains 8 cups of which 5 are red and 3 are blue. Two cups are taken out at random one by one without replacement. Find the probability that the cups are of different colors. 48. Mary received a box of chocolate bars which contains 8 chocolate bars with nuts. Mary takes out one bar at random. Then, she takes out another bar at random. Find the probability that Mary takes 2 chocolate bars with nuts. 49. There are 8 cards in an envelope numbered 1,3, 5, 7, 9, 11, 13 and 15. John takes two cards one by one without replacement. Find the probability that both cards are marked with prime numbers. 50. John has 5 shirts of which 2 are white and 3 are blue. He also has 6 ties of which 3 are yellow and 3 are blue. He also has 6 ties of which 3 are yellow and 3 are blue. One morning, John selects a shirt and a tie at random. Find the probability that he has chosen a white shirt and a yellow tie.
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