Probability Assignment

2021/8/17 HW1 – Intro to Probability

https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.hw1.html 1/2

Intro to Probability – Homework Assignment 1

Please solve the problems and type the solutions up using LateX and the template provided. Naming instructions for the file you will submit are contained in the file itself. Please justify your answers and don’t simply give the answer.

Problem 1 How many plate numbers can be created in California format DLLLDDD, where D stands for digit and L stands for letter? What if no repetitions are allowed in the digits?

Problem 2 A zip code consists of 5 digits. If the first cannot be the digit 0, how many zip codes can be generated?

Problem 3 How many letter arrangements can be made from the letters of the word Iowa? How about from the letters of Connecticut?

Problem 4 How many 5-card poker hands are there? (A regular deck has 52 cards).

Problem 5 Assuming that you can only move to the right or down, in how many ways can you get from the top left point to the bottom right one along the depicted grid?

Problem 6 If you need to split a class of 32 students in 8 groups of 4, in how many ways can you do it?

Home About Video Lectures Short Videos Problem Sets FAQ Resources Contact

https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/FnameLnameHWn.tex
https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/courseIndex.html
https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.about.html
2021/8/17 HW1 – Intro to Probability

https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.hw1.html 2/2

Problem 7 If a student is required to solve 8 out of 10 assigned problems, how many choices does she have? What if the first 4 problems are mandatory?

Problem 8 How many actual digit numbers exist? What if no two consecutive digits can be the same? How many numbers with at most digits exist? Numbers are to be understood as actuall numbers: 1 is a one digit number but 001 is not an actual number and certainly not a 3 digit number.

Problem 9 A total of 6 people need to be selected from a set of 10 twins of different families (20 people total). How many choices are there, if it is not allowed to select two siblings?

Problem 10 A total of 8 representatives need to be chosen from a group of 40 students, of which 24 are female and 16 are male. In how many ways can this be done? What if we require that there be at least 3 female and 3 male representatives?

Home About Video Lectures Short Videos Problem Sets FAQ Resources Contact

https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/courseIndex.html
https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.about.html

Our Service Charter

1. Professional & Expert Writers: Homework Free only hires the best. Our writers are specially selected and recruited, after which they undergo further training to perfect their skills for specialization purposes. Moreover, our writers are holders of masters and Ph.D. degrees. They have impressive academic records, besides being native English speakers.

2. Top Quality Papers: Our customers are always guaranteed of papers that exceed their expectations. All our writers have +5 years of experience. This implies that all papers are written by individuals who are experts in their fields. In addition, the quality team reviews all the papers before sending them to the customers.

3. Plagiarism-Free Papers: All papers provided by Homework Free are written from scratch. Appropriate referencing and citation of key information are followed. Plagiarism checkers are used by the Quality assurance team and our editors just to double-check that there are no instances of plagiarism.

4. Timely Delivery: Time wasted is equivalent to a failed dedication and commitment. Homework Free is known for timely delivery of any pending customer orders. Customers are well informed of the progress of their papers to ensure they keep track of what the writer is providing before the final draft is sent for grading.

5. Affordable Prices: Our prices are fairly structured to fit in all groups. Any customer willing to place their assignments with us can do so at very affordable prices. In addition, our customers enjoy regular discounts and bonuses.

6. 24/7 Customer Support: At Homework Free, we have put in place a team of experts who answer to all customer inquiries promptly. The best part is the ever-availability of the team. Customers can make inquiries anytime.