4. Ten friends realise that they all have their birthdays in the week 1-7thFebruary.(a) How many different configurations of birthdays are possible?(b) If it also true that every day that week is at least one of their birth-days, how many configurations are possible?(c) If there are exactly two days that week where it is none of their birth-days, how many configurations are possible?

Answered: Image /qna-images/answer/70633fea-dcc7-468d-9470-559bcab1dfa8.jpg

Answered: Ten friends realise that they all have…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(a) If repetition of digits is not allowed, how many four-digit numbers can be formed using the digits 1, 2, 3, 4, and 5? (b) How many of the numbers in part (a) begin with either of the digits 2, 3, or 4? (c) How many of the numbers in part (a) are even?
Suppose there are 10 students participating in a workshop that meets every day of a five-day work week. Each student must present a poster in exactly one of the days of the workshop, and every day of the workshop should have at least one poster presentation. If nk denotes the number of posters presented in day k of the workshop, what is the number of possible quintuples (n1,n2,n3,n4,n5)? I ll rate accordingly.
Twelve luxury cars (4 VW, 4 BMW and 4 Mercedes Benz) are booked by their owners for service at a workshop in Randburg. Suppose the mechanic services one car at any given time. In how many different ways may the cars be serviced in such a way that every BMW car is immediately preceded by a VW car?
Question 11 of 20 There are 17 players on a Calvinball team. At the start of the game, the 13 players on the field must be arranged in the form of a orde in how many dfteent wan can it be decided which 13 players will be on the field and in what order they will be at the start of the game? 17! 4 x 13! OB 17! - 4! O D. 12! 17! E. 13 x 4!
With solution and explanation
A computer programming section has 11 members. A team of 5 is to be chosen to work on a special project. (a) How many ways can the team be chosen? (b) Suppose there are 6 men and 5 women in the section. How many teams of 5 have no women? How many teams of 5 have one woman ? How many teams of 5 have two women? How many teams of 5 have at most two women? (c) Two team members refuse to work together on projects. The teams must include one or neither of them. Now how many teams of 5 can be chosen to work on the project?
36 customers arrive at exactly the same time. How many ways can the first 6 customers be chosen in the first hour, assuming that the 6 customers will get waited on at the exact same time?
"Question 3 (MaC)". (i) John has 5 toy cars and 4 toy buses that are all different from each other. John arranges these 9 toys in a line. Find the number of possible arrangements if: (a) (a) the cars and buses are arranged alternately. (B) the buses are all next to each other. (b) John randomly chooses 4 toys to take on holiday with him. Find (a) in how many ways John can choose the 4 toys. (B) the probability that his choices will include both his favourite car and his favourite bus. | (ii) Consider the function f(x) = x" +1 (a) Evaluate lim x→® x* +1 (b) Find the stationary point of the curve y = f(x) and determine its nature. (c) Find the point(s) of inflection of the curve y = f(x). (d) Sketch the curve y = f(x) showing all the features found above. Using your graph, find all values of k for which the equation kx² = 1-k has exactly one solution. (e)
Twenty-one girls and twenty-one boys took part in a mathematical compe- tition. It turned out that (a) Each contestant solved at most six problems, and (b) For each pair of a girl and a boy, there was at least one problem that both of them solved. Prove that there is a problem that was solved by at least three girls and at least three boys.

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