# MTH 221 Week 1 Assignment - Week 1 Connect Exercises

MTH 221 Week 1 Assignment - Week 1 Connect Exercises

MTH 221 Week 1 Assignment - Week 1 Connect Exercises

MTH 221 Week 1 Assignment - Week 1 Connect Exercises

MTH 221 Week 1 Assignment - Week 1 Connect Exercises

MTH 221 Week 1 Assignment - Week 1 Connect Exercises

1. A particular brand of shirt comes in 13 colors, has a male version and a female version, and comes in 3 sizes for each sex. How many different types of this shirt are made?

2. How many strings of five decimal digits

1. do not contain the same digit twice?

2. end with an even digit?

3. have exactly four digits that are 9’s?

3. How many strings of six uppercase English letters are there

1. if letters can be repeated?

2. if no letter can be repeated?

3. that start with X, if letters can be repeated?

4. that start with X, if no letter can be repeated?

5. that start and end with X, if letters can be repeated?

6. that start with the letters NE (in that order). if letters can be repeated?

7. that start and end with the letters NE (in that order), if letters can be repeated?

8. that start or end with the letters NE (in that order), if letters can be repeated?

4. In how many different orders can five runners finish a race if no ties are allowed?

5. How many bit strings of length 9 have

exactly three O s?

more O s than 1 s?

at least six 1 s?

at least three 1 s?

6. A club has 16 members

a) How many ways are there to choose four members of the club to serve on an executive committee?

b) How many ways are there to choose a president. vice president. secretary. and treasurer of the club, where no person can hold more than one office?

7. Five women and nine men are on the faculty in the mathematics department at a school

a) How many ways are there to select a committee of five members of the department if at least one woman must be on the committee?

b) How many ways are there to select a committee of five members of the department if at least one woman and at least one man must be on the committee?

8. Find the coefficient of in x16y4 in (x + y)20

9. What is the coefficient of x8 in (3 + x)12 ?

10. In how many different ways can seven elements be selected in order from a set with four elements when repetition is allowed?

11. How many ways are there to assign three jobs to twenty employees if each employee can be given more than one job?

12. How many solutions are there to the equation

x1+x2+x3+x4+x5 =21

where xi , i = 1, 2, 3, 4, 5, is a nonnegative integer such that

a) x1 ≥ 1?

b) x1 ≥ 3 for i= 1,2,3,4,5?

c) 0 ≤ x1 ≤ 3, 1 ≤ x2 < 4, and x3 ≥ 15?

d) 0 ≤ x1 ≤ 3, 1 ≤ x2 < 4, and x3 ≥ 15?

13. How many ways are there to distribute thirteen indistinguishable balls into eight distinguishable bins?

14. How many different strings can be made from the letters in MISSISSIPPI. using all the letters?

15. What is the probability that a five-card poker hand contains the nine of diamonds, the eight of clubs and the king of spades?

16. What is the probability that a fair die never comes up an even number when it is rolled four times?

17. Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding 5O.

18. What is the probability that Bo, Colleen, Jeff, and Rohini win the first, second, third, and fourth prizes, respectively, in a drawing if 48 people enter a contest and

MTH 221 Week 1 Assignment - Week 1 Connect Exercises

MTH 221 Week 1 Assignment - Week 1 Connect Exercises

MTH 221 Week 1 Assignment - Week 1 Connect Exercises

MTH 221 Week 1 Assignment - Week 1 Connect Exercises

1. A particular brand of shirt comes in 13 colors, has a male version and a female version, and comes in 3 sizes for each sex. How many different types of this shirt are made?

2. How many strings of five decimal digits

1. do not contain the same digit twice?

2. end with an even digit?

3. have exactly four digits that are 9’s?

3. How many strings of six uppercase English letters are there

1. if letters can be repeated?

2. if no letter can be repeated?

3. that start with X, if letters can be repeated?

4. that start with X, if no letter can be repeated?

5. that start and end with X, if letters can be repeated?

6. that start with the letters NE (in that order). if letters can be repeated?

7. that start and end with the letters NE (in that order), if letters can be repeated?

8. that start or end with the letters NE (in that order), if letters can be repeated?

4. In how many different orders can five runners finish a race if no ties are allowed?

5. How many bit strings of length 9 have

exactly three O s?

more O s than 1 s?

at least six 1 s?

at least three 1 s?

6. A club has 16 members

a) How many ways are there to choose four members of the club to serve on an executive committee?

b) How many ways are there to choose a president. vice president. secretary. and treasurer of the club, where no person can hold more than one office?

7. Five women and nine men are on the faculty in the mathematics department at a school

a) How many ways are there to select a committee of five members of the department if at least one woman must be on the committee?

b) How many ways are there to select a committee of five members of the department if at least one woman and at least one man must be on the committee?

8. Find the coefficient of in x16y4 in (x + y)20

9. What is the coefficient of x8 in (3 + x)12 ?

10. In how many different ways can seven elements be selected in order from a set with four elements when repetition is allowed?

11. How many ways are there to assign three jobs to twenty employees if each employee can be given more than one job?

12. How many solutions are there to the equation

x1+x2+x3+x4+x5 =21

where xi , i = 1, 2, 3, 4, 5, is a nonnegative integer such that

a) x1 ≥ 1?

b) x1 ≥ 3 for i= 1,2,3,4,5?

c) 0 ≤ x1 ≤ 3, 1 ≤ x2 < 4, and x3 ≥ 15?

d) 0 ≤ x1 ≤ 3, 1 ≤ x2 < 4, and x3 ≥ 15?

13. How many ways are there to distribute thirteen indistinguishable balls into eight distinguishable bins?

14. How many different strings can be made from the letters in MISSISSIPPI. using all the letters?

15. What is the probability that a five-card poker hand contains the nine of diamonds, the eight of clubs and the king of spades?

16. What is the probability that a fair die never comes up an even number when it is rolled four times?

17. Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding 5O.

18. What is the probability that Bo, Colleen, Jeff, and Rohini win the first, second, third, and fourth prizes, respectively, in a drawing if 48 people enter a contest and

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