Discrete Mathematics Answers

There are 10 stalls for animals in an exhibition. Three animals; lion, pussycat

and horse are to be exhibited. Animals of each kind are not less than 10 in

number. What is the possible number of ways of arranging the exhibition?

There are 10 stalls for animals in an exhibition. Three animals; lion, pussycat

and horse are to be exhibited. Animals of each kind are not less than 10 in

number. What is the possible number of ways of arranging the exhibition?

How many numbers of three digits can be formed with the digits 1, 2, 3, 4 and 5

if the digits in the same number are not repeated? How many such numbers are

possible between 100 and 10,000

A man, a woman, a boy, a girl, a dog, and a cat are walking down a long and

winding road one after the other.

(a) In how many ways can this happen?

(b) In how many ways can this happen if the dog comes first?

(c) In how many ways can this happen if the dog immediately follows the boy?

(d) In how many ways can this happen if the dog (and only the dog) is between

the man and the boy?

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.