UNIVERSITY OF BOTSWANA FACULTY OF SCIENCE DEPARTMENT OF MATHEMATICS MAT271 INTRODUCTION TO MATHEMATICAL STATISTICS TUTORIAL EXECISES 1 PART I. COUNTING PRINCIPLES I (1) A president and a treasurer are to be chosen from a student club consisting of 50 people. How many different choices of officers are possible if (a) there are no restrictions; (b) A will serve only if he is president; (c) B and C will serve together or not at all; (d) D and E will not serve together? (2) Four married couples have bought 8 scats in the same row for a concert. In how many different ways can they be seated (a) With no restrictions? (b) If each couple is to sit together? (c) If all the men sit together to the right of all the women? (3) You are going on a road trip with 4 friends in a car that fits 5 people. How many different ways can everyone sit if you have to drive the whole way? (4) In how many ways can 4 boys and 5 girls sit in a row if the boys and girls must alternate? (5) In how many ways can 5 different trees be planted in a circle? (6) You are deciding which awards you are going to display in your room. You have 8 awards, but you only have room to display 4 awards. Right now you are not worrying about how to arrange the awards, so the order does not matter. How many ways could you choose the 4 awards to display? (7) How many ways are there to select 3 candidates from 8 equally qualified recent graduates for openings in an accounting firm? (8) How many different ways can the gold, silver, and bronze medals be awarded in an Olympic event with 12 athletes competing? (9) How many different ways could you score a 70% on a 10-question test. where each question is weighted equally and is either right or wrong?
UNIVERSITY OF BOTSWANA FACULTY OF SCIENCE DEPARTMENT OF MATHEMATICS MAT271 INTRODUCTION TO MATHEMATICAL STATISTICS TUTORIAL EXECISES 1 PART I. COUNTING PRINCIPLES I (1) A president and a treasurer are to be chosen from a student club consisting of 50 people. How many different choices of officers are possible if (a) there are no restrictions; (b) A will serve only if he is president; (c) B and C will serve together or not at all; (d) D and E will not serve together? (2) Four married couples have bought 8 scats in the same row for a concert. In how many different ways can they be seated (a) With no restrictions? (b) If each couple is to sit together? (c) If all the men sit together to the right of all the women? (3) You are going on a road trip with 4 friends in a car that fits 5 people. How many different ways can everyone sit if you have to drive the whole way? (4) In how many ways can 4 boys and 5 girls sit in a row if the boys and girls must alternate? (5) In how many ways can 5 different trees be planted in a circle? (6) You are deciding which awards you are going to display in your room. You have 8 awards, but you only have room to display 4 awards. Right now you are not worrying about how to arrange the awards, so the order does not matter. How many ways could you choose the 4 awards to display? (7) How many ways are there to select 3 candidates from 8 equally qualified recent graduates for openings in an accounting firm? (8) How many different ways can the gold, silver, and bronze medals be awarded in an Olympic event with 12 athletes competing? (9) How many different ways could you score a 70% on a 10-question test. where each question is weighted equally and is either right or wrong?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:UNIVERSITY OF BOTSWANA
FACULTY OF SCIENCE
DEPARTMENT OF MATHEMATICS
MAT271 INTRODUCTION TO MATHEMATICAL STATISTICS
TUTORIAL EXECISES 1
PART I. COUNTING PRINCIPLES
I
(1) A president and a treasurer are to be chosen from a student club consisting
of 50 people. How many different choices of officers are possible if
(a) there are no restrictions;
(b) A will serve only if he is president;
(c) B and C will serve together or not at all;
(d) D and E will not serve together?
(2) Four married couples have bought 8 scats in the same row for a concert. In
how many different ways can they be seated
(a) With no restrictions?
(b) If each couple is to sit together?
(c) If all the men sit together to the right of all the women?
(3) You are going on a road trip with 4 friends in a car that fits 5 people. How
many different ways can everyone sit if you have to drive the whole way?
(4) In how many ways can 4 boys and 5 girls sit in a row if the boys and girls
must alternate?
(5) In how many ways can 5 different trees be planted in a circle?
(6) You are deciding which awards you are going to display in your room. You
have 8 awards, but you only have room to display 4 awards. Right now you
are not worrying about how to arrange the awards, so the order does not
matter. How many ways could you choose the 4 awards to display?
(7) How many ways are there to select 3 candidates from 8 equally qualified
recent graduates for openings in an accounting firm?
(8) How many different ways can the gold, silver, and bronze medals be awarded
in an Olympic event with 12 athletes competing?
(9) How many different ways could you score a 70% on a 10-question test.
where each question is weighted equally and is either right or wrong?
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