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?
Homework Answers
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1. How many decorations are there using
12
blue balloons,
9
green lanterns and
6
red...
6. (The truck contains 6 blue balloons, 6 red balloons and 8 green balloons. Do not...
6. (The truck contains 6 blue balloons, 6 red balloons and 8 green balloons. Do not simplify your answers. Leave in Combinatorics format. In how many ways can 6 balloons escape from the truck so that: At least 4 red balloons escape? at most two blue balloons escape? no green balloons escape? the balloons that escape are all the same color?
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?
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...
There are red, blue, white and green marbles. How many different ways are there to fill...
There are red, blue, white and green marbles. How many different ways are there to fill a bag with 10 marbles if there is the constraint that there are either white or green marbles in the bag but never both. So there can be white marbles in it or there can be green marbles in it or neither or them but never both.
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...
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6...
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6 red boxes labelled 1 to 6 and 6 blue boxes labelled 1 to 6, such that the blue be with label i and the red box with labeli receive the same number of balls, for every ie (1,2,3,4,5, 6}? [10 marks
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6 red boxes labelled 1 to 6 and...
6 different books are to be distributed among the 10 students in a class. A student...
6 different books are to be distributed among the 10 students in a class. A student can receive multiple books; for example, it's possible that one student receives all 6 of them. How many ways are there to distribute the books: (a) How many ways are there to distribute the books? (b) ... if Alice gets at least one book? (c) ... if only Alice, Bob, and Chloe receive books? (d) ... if only Alice, Bob, and Chloe receive books...
Kelly has different books to arrange on a shelf; 2 blue, 4 green, and 3 red....
Kelly has different books to arrange on a shelf; 2 blue, 4 green, and 3 red. Answer parts a through e below. (a) In how many ways can the books be arranged on a shelf? way(s) (Type a whole number.) (b) If books of the same color are to be grouped together, how many arrangements are possible? way(s) (Type a whole number.) (c) In how many distinguishable ways can the books be arranged if books of the same color are...
There are 15 red balls and 10 blue balls. 1) How many ways are there to...
There are 15 red balls and 10 blue balls. 1) How many ways are there to choose one ball to be placed on a chair and one ball to be placed on a desk? (My original answer was 600) 2) How many ways are there to choose one ball to be placed on a chair and one ball to be placed on a desk if both balls cannot be the same color? (My original answer was 150) 3) How many...
1. Find a1s for each of the following generating functions: contains 8 red, 8 white, 8 blue, and 5 green balls, which are identical cept for color. How many ways are there to select 20 balls? 2....
1. Find a1s for each of the following generating functions: contains 8 red, 8 white, 8 blue, and 5 green balls, which are identical cept for color. How many ways are there to select 20 balls? 2. A b ox 3. Find a1e for each of the following generating functions:
1. Find a1s for each of the following generating functions: contains 8 red, 8 white, 8 blue, and 5 green balls, which are identical cept for color. How many ways...
6. (The truck contains 6 blue balloons, 6 red balloons and 8 green balloons. Do not simplify your answers. Leave in Combinatorics format. In how many ways can 6 balloons escape from the truck so that: At least 4 red balloons escape? at most two blue balloons escape? no green balloons escape? the balloons that escape are all the same color?
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?
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...
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...
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6 red boxes labelled 1 to 6 and 6 blue boxes labelled 1 to 6, such that the blue be with label i and the red box with labeli receive the same number of balls, for every ie (1,2,3,4,5, 6}? [10 marks
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6 red boxes labelled 1 to 6 and...
6 different books are to be distributed among the 10 students in a class. A student can receive multiple books; for example, it's possible that one student receives all 6 of them. How many ways are there to distribute the books: (a) How many ways are there to distribute the books? (b) ... if Alice gets at least one book? (c) ... if only Alice, Bob, and Chloe receive books? (d) ... if only Alice, Bob, and Chloe receive books...
Kelly has different books to arrange on a shelf; 2 blue, 4 green, and 3 red. Answer parts a through e below. (a) In how many ways can the books be arranged on a shelf? way(s) (Type a whole number.) (b) If books of the same color are to be grouped together, how many arrangements are possible? way(s) (Type a whole number.) (c) In how many distinguishable ways can the books be arranged if books of the same color are...
1. Find a1s for each of the following generating functions: contains 8 red, 8 white, 8 blue, and 5 green balls, which are identical cept for color. How many ways are there to select 20 balls? 2. A b ox 3. Find a1e for each of the following generating functions:
1. Find a1s for each of the following generating functions: contains 8 red, 8 white, 8 blue, and 5 green balls, which are identical cept for color. How many ways...
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