guided exercise 11, pg. 225 a. evaluate 31. 31 = 3, 2, 1 = 6 b. in how many different ways can three objects be arran...
guided exercise 11, pg. 225
a. evaluate 31. 31 = 3, 2, 1 = 6
b. in how many different ways can three objects be arranged in order? how many choices do you have for the first position? for the second nd position? for the third position?
you have three choices for the first pos. two for the second pos. and one for the third pos. by the multiplication you have (3) (2) (1) = 31 = 6 arrangements
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guided exercise 11, pg. 225 a. evaluate 31. 31 = 3, 2, 1 = 6 b. in how many different ways can three objects be arran...
Principles of Counting: You have a ten-volume set of books. a) How many different ways can...
Principles of Counting: You have a ten-volume set of books. a) How many different ways can the books be arranged? b) How many of these arrangements have Volumes 1, 2, and 3 side by side in any order? c) How many of these arrangements have Volumes 1, 2, and 3 side by side in that order?
3). In how many ways can 6 students be seated in a row of 6 chairs...
3). In how many ways can 6 students be seated in a row of 6 chairs if Jack insists on sitting in the first chair? 4). A president, a treasurer, and a secretary are to be chosen from a committee with forty members. In how many ways could the three officers can be chosen? 5). In how many ways can 7 books be chosen from a group of nine? 9). Suppose that a department contain 13 men and 15 women....
1. How many different ways can you have r numbers 1 sum up to a number...
1. How many different ways can you have r numbers 1 sum up to a number n? These are called compositions of a number n and it is easy to calculate from our understanding of binomial coefficients. So the number of compositions of 4 into 3 parts will be 1+1+2, 1+2+1, and 2+1+1. Note how we think of 1+1+2 and 1+2+1 as different-because in the first case, the first number is 1, second is 1 and third is 2, while...
Exercise 9. From a box of 10 lightbulbs, you are to remove 4. How many different...
Exercise 9. From a box of 10 lightbulbs, you are to remove 4. How many different sets of 4 lightbulbs could you remove? A talent contest has 8 contestants. Judges must award prizes for first, second, Exercise 10. and third places, with no ties. (a) In how many different ways can the judges award the 3 prizes? (b) How many different groups of 3 people can get prizes?
A contest of 10 girls has 3 winners. In how many ways can you choose 3...
A contest of 10 girls has 3 winners. In how many ways can you choose 3 winners if; A. You select a first, second, and third place? B. You select a group of 3 winners?
Part B(COMBINATORICS) LEAVE ALL ANSWERA IN TERMS OF C(nr) or factorials Q4(a)6) In how many ways can you arrange the letters in the word INQUISITIVE? in how many of the above arrangements, U i...
Part B(COMBINATORICS) LEAVE ALL ANSWERA IN TERMS OF C(nr) or factorials Q4(a)6) In how many ways can you arrange the letters in the word INQUISITIVE? in how many of the above arrangements, U immediately follows Q? Q4. (b)Suppose you are a math major who is behind in requirements and you must take 4 math courses and therefore next semester. Your favorite professor, John Smith, is teaching 2 courses next semester you "must" take at least one of them. If there...
Question 7 (1 point) In how many ways can 4 female students and 3 male students...
Question 7 (1 point) In how many ways can 4 female students and 3 male students be selected from a class with 17 female and 13 male students? Your Answer: Answer Question 8 (1 point) In how many ways can a president, vice-president, treasurer, and secretary be selected from a class of 55 students? Your Answer: Answer Question 9 (1 point) Suppose you want to purchase a new wardrobe that has a variety of clothes that can all be worn...
3. Suppose my graph theory class has 12 different students, of which 6 are under- grads and 6 are graduate students. (a). How many ways can I choose at least 4 but no more than 8 of my students to ta...
3. Suppose my graph theory class has 12 different students, of which 6 are under- grads and 6 are graduate students. (a). How many ways can I choose at least 4 but no more than 8 of my students to take a field trip to the library? (b). I want to repeat part (a), but I want to be sure to take at least 2 undergrads. (c). I have 3 different final projects for them to work on (projects A,...
please illustrate each stepbof the solution so I can understand thank you 4) Given the diagram 2 7 3 6 4 (a) Up to symmetries, in how many ways can we paint the numbered vertices, if tw...
please illustrate each stepbof the solution so I can
understand
thank you
4) Given the diagram 2 7 3 6 4 (a) Up to symmetries, in how many ways can we paint the numbered vertices, if two colors (red and blue) are available? (b) How many ways, if additionally we want that at most two numbered vertices are painted red?
4) Given the diagram 2 7 3 6 4 (a) Up to symmetries, in how many ways can we paint...
1. How many different ways can you have r numbers 1 sum up to a number n? These are called compositions of a number n and it is easy to calculate from our understanding of binomial coefficients. So the number of compositions of 4 into 3 parts will be 1+1+2, 1+2+1, and 2+1+1. Note how we think of 1+1+2 and 1+2+1 as different-because in the first case, the first number is 1, second is 1 and third is 2, while...
Exercise 9. From a box of 10 lightbulbs, you are to remove 4. How many different sets of 4 lightbulbs could you remove? A talent contest has 8 contestants. Judges must award prizes for first, second, Exercise 10. and third places, with no ties. (a) In how many different ways can the judges award the 3 prizes? (b) How many different groups of 3 people can get prizes?
Part B(COMBINATORICS) LEAVE ALL ANSWERA IN TERMS OF C(nr) or factorials Q4(a)6) In how many ways can you arrange the letters in the word INQUISITIVE? in how many of the above arrangements, U immediately follows Q? Q4. (b)Suppose you are a math major who is behind in requirements and you must take 4 math courses and therefore next semester. Your favorite professor, John Smith, is teaching 2 courses next semester you "must" take at least one of them. If there...
Question 7 (1 point) In how many ways can 4 female students and 3 male students be selected from a class with 17 female and 13 male students? Your Answer: Answer Question 8 (1 point) In how many ways can a president, vice-president, treasurer, and secretary be selected from a class of 55 students? Your Answer: Answer Question 9 (1 point) Suppose you want to purchase a new wardrobe that has a variety of clothes that can all be worn...
3. Suppose my graph theory class has 12 different students, of which 6 are under- grads and 6 are graduate students. (a). How many ways can I choose at least 4 but no more than 8 of my students to take a field trip to the library? (b). I want to repeat part (a), but I want to be sure to take at least 2 undergrads. (c). I have 3 different final projects for them to work on (projects A,...
please illustrate each stepbof the solution so I can
understand
thank you
4) Given the diagram 2 7 3 6 4 (a) Up to symmetries, in how many ways can we paint the numbered vertices, if two colors (red and blue) are available? (b) How many ways, if additionally we want that at most two numbered vertices are painted red?
4) Given the diagram 2 7 3 6 4 (a) Up to symmetries, in how many ways can we paint...
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