Mth202 Assignment No. 5 Solution
Tuesday, June 28, 2011 Posted In Mth Edit ThisAssignment#5 Of MTH202 (Spring 2011)
Maximum Marks: 15
Due Date: June 28, 2011
DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
•To solve this assignment, you should have good command over 31 -35 lectures.
• Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in the 31 to 35 lectures.
• Upload assignments properly through LMS, No Assignment will be accepted through email.
• Write your ID on the top of your solution file.
• Don’t use colorful back grounds in your solution files.
• Use Math Type or Equation Editor etc for mathematical symbols.
• You should remember that if we found the solution files of some students are same then we will reward zero marks to all those students.
• Try to make solution by yourself and protect your work from other students, otherwise you and the student who send same solution file as you will be given zero marks.
• Also remember that you are supposed to submit your assignment in Ms-Word format any other like scan images etc will not be accepted and we will give zero marks correspond to these assignments.
Question 1; Mark: 5
A company manager wants to hire 4 people from a group of 10 applicants, 4 men and 6 women, all of whom are equally qualified to fill the position. If he selects the four at random, what is the probability that
i. All four will be women
ii. At least two will be men?
Question 2; Marks: 5
How many ways are there to select a committee to develop a discrete mathematics course at a university if the committee is to consist of four faculty members from the mathematics department and three from the computer science department, if there are 10 faculty members of the mathematics department and 12 of the computer science department?
Question 3; Marks: 5
Suppose that there are 1807 students at university. Of these, 453 are taking a course in computer science, 567 are taking a course in mathematics, and 299 are taking a courses in both computer science and mathematics .How many are not taking a course in either computer science or in mathematics?
Maximum Marks: 15
Due Date: June 28, 2011
DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
•To solve this assignment, you should have good command over 31 -35 lectures.
• Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in the 31 to 35 lectures.
• Upload assignments properly through LMS, No Assignment will be accepted through email.
• Write your ID on the top of your solution file.
• Don’t use colorful back grounds in your solution files.
• Use Math Type or Equation Editor etc for mathematical symbols.
• You should remember that if we found the solution files of some students are same then we will reward zero marks to all those students.
• Try to make solution by yourself and protect your work from other students, otherwise you and the student who send same solution file as you will be given zero marks.
• Also remember that you are supposed to submit your assignment in Ms-Word format any other like scan images etc will not be accepted and we will give zero marks correspond to these assignments.
Question 1; Mark: 5
A company manager wants to hire 4 people from a group of 10 applicants, 4 men and 6 women, all of whom are equally qualified to fill the position. If he selects the four at random, what is the probability that
i. All four will be women
ii. At least two will be men?
Question 2; Marks: 5
How many ways are there to select a committee to develop a discrete mathematics course at a university if the committee is to consist of four faculty members from the mathematics department and three from the computer science department, if there are 10 faculty members of the mathematics department and 12 of the computer science department?
Question 3; Marks: 5
Suppose that there are 1807 students at university. Of these, 453 are taking a course in computer science, 567 are taking a course in mathematics, and 299 are taking a courses in both computer science and mathematics .How many are not taking a course in either computer science or in mathematics?
SOLUTION:
- All four will be women
- At least two will be men?
C(10,4)
=10!/4!(10-4)!
=10*9*8*7*6*! / 4*3*2*1*(6!)
=5040*6*5*4*3*2*1 / 24*6*5*4*3*2*1
=5040*720 / 24*720 =362800 / 17280
=210
C(6,4)
=6!/4!(6-4)!
=6*5*4*3*2*1 / 4*3*(2!)
=720 / 24(2*1) =720/48
=15
C(8,2)
=8! / 2!(8-2)! =8*7*6*5*4*3*2*1 / 2 *1(6!)
=40320 / 2(720)
=28
How many ways are there to select a committee to develop a discrete mathematics course at a university if the committee is to consist of four faculty members from the mathematics department and three from the computer science department, if there are 10 faculty members of the mathematics department and 12 of the computer science department?
C(12,4).C (10,3)
=12! / 4! (12-4)! . 10! / 3! (10-3)!
=12*11*10*9*8! / 4*3*2*1(8!). 10*9*8*7! / 3*2*1 (7!)
=11880 / 24 .720/6
=495.120
=59400
Suppose that there are 1807 students at university. Of these, 453 are taking a course in computer science, 567 are taking a course in mathematics, and 299 are taking a courses in both computer science and mathematics .How many are not taking a course in either computer science or in mathematics?
N(U)=1807
N(m)=567
N(C ∩ m)=299
N(cUm)=?
N(cUm)=n(C)+n (m) –n (C∩m)
=453+567-299
=721
N(cUm)-n(U) –n (cUm)
=1807-721
=1088
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Another solution: Mth302 Assignment vusolution
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Another solution: Mth302 Assignment vusolution
