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5) (a) In how many ways can we distribute 10 different chocolates to 4 children so that every chi...
1. Multiplication theorem There are 20 toys and 12 children. We want to distribute the toys...
1. Multiplication theorem There are 20 toys and 12 children. We want to distribute the toys to the children. In each of the cases below, count how many ways can we distribute the toys. (Hint: think, what are my boxes and how can I fill them?). Please show your work. You can leave the expressions as is, so no nieed to do the calculations (a) If cach child gets cxactly one toy. b) Every toy is given out and it...
Problem 2 a) In how many ways can 6 women and 5 men line up so...
Problem 2 a) In how many ways can 6 women and 5 men line up so that no two men are next to one another? b) In how many ways can 7 different pairs of twins line up so that twins must be next to one another? c) In how many ways can 7 women and 10 men sit at a circular table so that no two women are sitting side by side? d) How many strings of length 5...
In how many ways can 15 red marbles and 17 blue marbles be distributed to 6...
In how many ways can 15 red marbles and 17 blue marbles be distributed to 6 children if each child is to receive at least one blue marble and at least 2 red marbles? In how many ways can 32 different books be placed on four shelves so that there is at least one book on each shelf?
You want to distribute 100 gold coins among 20 different people. How many ways can he...
You want to distribute 100 gold coins among 20 different people. How many ways can he do this if the gold coins are all... (g) identical but instead are distributed into 20 identical piggy banks such that no piggy bank is empty. (h) different and each person gets exactly five coins. (i) identical and each person gets exactly five coins. (j) different and the Leader gets ten pieces while the other people can get any number of pieces
1. Eight different gifts are to be distributed among three children, a) How many distinct results...
1. Eight different gifts are to be distributed among three children, a) How many distinct results are possible? b) How many distinct results are possible if every child receives at least one gift? Hint. Note that "at least one child does not get anything" means "exactly one child does not get anything" or "exactly two do not get anything" 2. There are five flavors of ice cream: C, M, B, S and V a) How many variations of three scoop...
Ex 1 We have 8 people in the family. (a) We got 3 different gifts from...
Ex 1 We have 8 people in the family. (a) We got 3 different gifts from Santa under the Christmas tree (yes, somebody did not behave well this year :0. We do not know who these gifts are for. In how many ways can we distribute the gifts? (cach person may get more than one gift) (a) We got 3 different gifts from Santa under the Christmas tro. We do not know who thesc gifts are for. In how many...
5. (3 points) You have 16 pieces of candy to distribute to 7 people (all persons are distinguishable from one another). How many ways are there to distribute the candy if -each piece of candy is diff...
5. (3 points) You have 16 pieces of candy to distribute to 7 people (all persons are distinguishable from one another). How many ways are there to distribute the candy if -each piece of candy is different? -each piece of candy is identical? -each piece of candy is identical and four people get at least one piece of candy each, while the three remaining people get none
5. (3 points) You have 16 pieces of candy to distribute to 7...
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...
1. How many decorations are there using 12 blue balloons, 9 green lanterns and 6 red...
1. How many decorations are there using 12 blue balloons, 9 green lanterns and 6 red ribbons in a row, such that no two ribbons are next to each other? 2. In how many ways can one distribute seven different gifts among 10 children if no child is to receive more than one gift?
How many possibilities are there to distribute 15 letters among 5 people so that each of...
How many possibilities are there to distribute 15 letters among 5 people so that each of them receive at least one letter? (The letters are distinguishable)
1. Multiplication theorem There are 20 toys and 12 children. We want to distribute the toys to the children. In each of the cases below, count how many ways can we distribute the toys. (Hint: think, what are my boxes and how can I fill them?). Please show your work. You can leave the expressions as is, so no nieed to do the calculations (a) If cach child gets cxactly one toy. b) Every toy is given out and it...
In how many ways can 15 red marbles and 17 blue marbles be distributed to 6 children if each child is to receive at least one blue marble and at least 2 red marbles? In how many ways can 32 different books be placed on four shelves so that there is at least one book on each shelf?
1. Eight different gifts are to be distributed among three children, a) How many distinct results are possible? b) How many distinct results are possible if every child receives at least one gift? Hint. Note that "at least one child does not get anything" means "exactly one child does not get anything" or "exactly two do not get anything" 2. There are five flavors of ice cream: C, M, B, S and V a) How many variations of three scoop...
Ex 1 We have 8 people in the family. (a) We got 3 different gifts from Santa under the Christmas tree (yes, somebody did not behave well this year :0. We do not know who these gifts are for. In how many ways can we distribute the gifts? (cach person may get more than one gift) (a) We got 3 different gifts from Santa under the Christmas tro. We do not know who thesc gifts are for. In how many...
5. (3 points) You have 16 pieces of candy to distribute to 7 people (all persons are distinguishable from one another). How many ways are there to distribute the candy if -each piece of candy is different? -each piece of candy is identical? -each piece of candy is identical and four people get at least one piece of candy each, while the three remaining people get none
5. (3 points) You have 16 pieces of candy to distribute to 7...
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...
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