Discrete Mathematics Answers

A person has 8 children of them he takes 3 at a time to a circus. He does not take

the same three children twice to the circus. How many times he will have to go

to circus to ensure that every three children have seen the circus together? In

this case find the number of times a particular child has visited the circus.

From 8 men and 4 women and team of 5 is to be formed. In how many ways can

this be done so as to include at least one woman?

group of 30 people have been trained as astronauts to go on the first mission

to Mars. How many ways are there to select a crew of six people to go on this

mission (assuming that all crew members have the same job)?

In how many ways can 20 students out of a class of 32 be chosen to attend class

on a late Thursday afternoon (and take notes for the others) if

(a) Paul refuses to go to class?

(b) Michelle insists on going?

(c) Jim and Michelle insist on going?

(d) either Jim or Michelle (or both) go to class?

(e) just one of Jim and Michelle attend?

(f) Paul and Michelle refuse to attend class together?

Wandana is going to toss a coin eight times. In how many ways can she get five

heads and three tails

Suppose that a saleswoman has to visit eight different cities. She must begin her

trip in a specified city, but she can visit the other seven cities in any order she

wishes. How many possible orders can the saleswoman use when visiting these

cities?

In how many ways can 10 different examination papers be scheduled so that

(i) the best and the worst always come together?

(ii) the best and the worst never come together?

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?