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use generating functions to find the number of ways to choose a dozen bagels from three varieties-egg salty and
let x be the random variable whose value is n if the first success occurs on the nth trial when independent bernoulli
in the example of tossing two quarters what is the probability that at least one head is obtained that coin a is a head
consider the situation described in exercise 16a find the probability of the event that exactly one of the colors that
a how many positive two-digit integers are multiples of 3b what is the probability that a randomly chosen positive
a combination lock requires three selections of numbers each from 1 through 39 suppose the lock is constructed in such
a group of eight people are attending the movies togethera two of the eight insist on sitting side-by-side in how many
an interesting use of the inclusionexclusion rule is to check survey numbers for consistency for example suppose a
a if repeated divisions by 20483 are performed how many distinct remainders can be obtainedb when 520483 is written as
suppose six pairs of similar-looking boots are thrown together in a pile how many individual boots must you pick to be
a explain how to find a recurrence relation for the number of bit strings of length n not containing two consecutive
a what is dynamic programming and how are recurrence relations used in algorithms that follow this paradigmb explain
in graphs are represented by drawings define each graph formally by specifying its vertex set its edge set and a table
use the graph of example 1016 to determinea whether sports illustrated contains printed writingb whether poetry
find three other winning sequences of moves for the vegetarians and the cannibals in example 1017example 1017using a
another famous puzzle used as an example in the study of artificial intelligence seems first to have appeared in a
solve the vegetarians-and-cannibals puzzle for the case where there are three vegetarians and three cannibals to be
a in a simple graph must every vertex have degree that is less than the number of vertices in the graph whyb can there
prove that every nontrivial tree has at least two vertices of degree 1 by filling in the details and completing the
how many components are there in the n-tuples in the table obtained by applying the join operator j3 to two tables with
let r be a relation on a set a with n elements if there are k nonzero entries in mr the matrix representing r how many
find the smallest relation containing the relation 1 2 1 4 3 3 4 1 that isa reflexive and transitiveb symmetric and
which of these relations on the set of all people are equivalence relations determine the properties of an equivalence
algorithms have been devised that use on28 bit operations to compute the boolean product of two n times n zero-one
define three equivalence relations on the set of students in your discrete mathematics class different from the