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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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Suppose there are 5 men and 8 women qualified to be members of a new committee of 6 people, includinga president, a vice-president, and a secretary.(a) How many different ways do you have to pick a president, vice-president and secretary if you need atleast 1 men and 1 women? Does the order matter? Why?(b) How many different committees can you form with at least 3 women? Does the order matter? Why?
(3) In how many ways can 5 boys and 2 girls sit in a row if just the girls are to sit together?
A student works in a bookstore where he is required to work at least four and at most five days a week, at least one of which has to be a weekend day (Saturday or Sunday). How many different weekly work schedules can this student have?
How many different meals can occur when there are 10 different salads, 23 different deserts, and 5 main dishes. You can choose one main dish one salad and two deserts – no duplication on the deserts.
There are twenty marbles of similar colour and size where each marble is labelled with a number from 1 to 20. Find the number of ways to (i) select eight marbles such that five of them are labelled with odd numbers and the rest with even numbers, (ii) arrange six marbles in a row such that the first four marbles are labelled with odd numbers and the rest with even numbers.
You have 50 of each of the following kinds of jellybeans: red, orange, green, yellow. The jellybeans of each color are identical. In how many ways can you put all the jellybeans in a row such that no two colors come together?
Suppose that the captain of a ship that is in distress must send a total of eleven different signals in succession. The eleven signals com- prise of 4 blue light signals (B1, B2, B3 and B4), 4 purple light signals (P1, P2, P3 and P4) and 3 red light signals (R1, R2 and R3). He must send the signals one after another at 1 minute intervals. In how many different ways may the captain send the signals if the purple light signals are the first 4 signals and the red light signals are the last 3 signals? [Answer]
A total of 50 students are in a class and they are to be divided into groups of 5. How many different combinations of students are possible?
With a short time remaining in the day, a delivery driver has time to make deliveries to 6 different locations among the 7 locations remaining. How many different routes are possible?
how many ways to are there for eight men and ten women to stand in a line so that there would be exactly two women followed by at least one man?
Suppose we want to choose 4 objects, without replacement, from 17 distinct objects. (a) If the order of the choices is not relevant, how many ways can this be done? (b) If the order of the choices is relevant, how many ways can this be done?
Suppose 10 baseball players are available to be drafted by 4 teams where each team might win any number of these players. In how many ways can these 10 players be drafted?

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