Discrete Mathematics Answers

How many different sequences, each of length r, can be formed using elements

from A if

(a) elements in the sequence may be repeated?

(b) all elements in the sequence must be distinct?

In how many ways can the letters of the English alphabet be arranged so that

there are exactly ten letters between a and z?

There are 7! = 5040 ways in which seven people can form a line. In how many

ways can seven people form a circle

How many pairs of dance partners can be selected from a group of 12 women

and 20 men

Let A consist of all 52 cards in an ordinary deck of playing cards. Suppose that

this deck is shuffled and a hand of five cards is dealt. A list of cards in this hand,

in the order in which they were dealt, is a permutation of A taken five at a tim

Let R={(1,2),(2,1),(2,3),(3,4),(4,1) } be a relation on the A={1,2,3,4}. Find the transitive closure of R using Warshall’s algorithm.

Determine whether f : Z × Z → Z is onto if f(m,n)= m-n

Let a and b be two cardinal numbers. Modify Cantor’s definition of a < b to define a ≤ b. (Hint: Examine what happens if you drop condition (a) from Cantor’s definition of a < b.) 2. Prove that a ≤ a. 3. Prove that if a ≤ b and b ≤ c, then a ≤ c. 4. Do you think that a ≤ b and b ≤ a imply

a = b? Explain your reasoning. (Hint: This is not as trivial as it might look.)

How many positive integers less than 100 is not a factor of 2,3 and 5?

) How many ways are there for eight men and five women to stand in a line so that no two women stand next to each other?