How many possibilities are there to distribute 15 letters among 5 people so that each of...
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...
How many ways are there to distribute 8 identical apples, 6 oranges, and 7 pears among 3 different people.. Without restriction? With each person getting at least one pair? Please explain this well, and don't write it out in chicken scratch.
5) (a) In how many ways can we distribute 10 different chocolates to 4 children so that every child gets at least one chocolate? (b) In how many ways can we distribute 5 different chocolates to 9 children so that every child gets at most one chocolate?
5) (a) In how many ways can we distribute 10 different chocolates to 4 children so that every child gets at least one chocolate? (b) In how many ways can we distribute 5...
How many subsets are there of 5 letters? How many contain at least one letter, but not all of the letters {a, b, c, d, e}?
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...
A password consists of 4 letters among 26 lower-case English alphabet letters and 10 digits: 0,1,...,9. (i) How many different passwords that contain at least one digit can be formed? (ii) How many different passwords that contain at least one digit and at least one letter can be formed?
9.55. We distribute 15 books among four students so that all allocations are equally likely. What is the probability that 1. the first student gets at least 2 books? 2. the first or the last student gets at least two books? 3. no one gets less than three books?
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
In how many ways can 22 identical bottles of soda be distributed among four people, disregarding the order of distribution, so that each person gets at least one bottle? 34.
1. (5) Suppose we have a set of small wooden blocks showing the 26 letters of the English alphabet, one letter per block. (Think of Scrabble tiles.) Our set includes 10 copies of each letter. We place them into a bag and draw out one block at a time. (a) If we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) Now suppose we just toss...