# Answer in Statistics and Probability for Nghelo #241337

a.

To find the required solution, the concept of permutations is applied. It is given by;

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Answer in Statistics and Probability for Nghelo #241337
Just from $13/Page “{}^n{P}_k=\frac{n!}{(n-k)!}” n= total number of elements in a set. k= number of selected elements arranged in a specific order To form three-digit numbers from the digits 2,3,5,6,7 and 9, there are n=6 digits and k=3. Therefore, “{}^6{P}_3=\frac{6!}{(6-3)!}=\frac{6!}{3!}=6*5*4=120” The number of three-digit numbers which can be formed from the digits 2,3,5,6,7 and 9 is 120 b. For the numbers formed to be less than 500, the 100th’s place must either be 2 or 3. This is described in the cases below; Case 1: 2 is in the 100th’s place. They have already put the digit 2 in the 100th’s place. There remains 5 distinct digits to occupy the 10th’s place. In the unit’s place, 4 distinct digits may occupy this place apart from 2 and the digit in the 10th’s place. Therefore, total number of combinations for this case =1 * 5 * 4=20 Case 2: 3 is in the 100th’s place. The digit 3 is already in the 100th’s place hence there are 5 distinct digits that may occupy the 10th’s place and 4 distinct digits to occupy the unit’s place apart from 3 and the digit in the 10th’s place. Thus, total number of combinations=1 * 5 * 4=20. Total number of combinations without repeating the digits =20+20=40. So, the total number of three-digit numbers formed that are less than 500 is 40. c. For the numbers formed by the digits 2,3,5,6,7 and 9 to be even, the unit’s digit must be 2 or 6.This can be expressed in two cases as below; Case 1; numbers ending with 2. Since 2 is already in the unit’s place, some other digit should occupy the 10th’s place. There are 5 other digits which can occupy this place. Let’s come to 100th’s place. Apart from 2 and the digit that is already put in the 10th’s place, there are 4 distinct digits which may now occupy the 100th’s place. Thus, total number of combinations = 4 * 5 * 1 = 20 Case 2: Numbers ending with 6. The digit 6 is already in the unit’s place. Of the remaining 5 distinct digits, another digit should occupy the 10th’s place. In the 100th’s place, 4 distinct digits may occupy this place apart from 6 and the digit in the 10th’s place. Therefore, total number of combinations for this case =4 * 5 * 1=20 Thus, total number of even numbers formed without the digits being repeated is 20+20=40 There are 40 even numbers formed. # What Will You Get? We provide professional writing services to help you score straight A’s by submitting custom written assignments that mirror your guidelines. #### Premium Quality Get result-oriented writing and never worry about grades anymore. We follow the highest quality standards to make sure that you get perfect assignments. #### Experienced Writers Our writers have experience in dealing with papers of every educational level. You can surely rely on the expertise of our qualified professionals. #### On-Time Delivery Your deadline is our threshold for success and we take it very seriously. We make sure you receive your papers before your predefined time. #### 24/7 Customer Support Someone from our customer support team is always here to respond to your questions. So, hit us up if you have got any ambiguity or concern. #### Complete Confidentiality Sit back and relax while we help you out with writing your papers. We have an ultimate policy for keeping your personal and order-related details a secret. #### Authentic Sources We assure you that your document will be thoroughly checked for plagiarism and grammatical errors as we use highly authentic and licit sources. #### Moneyback Guarantee Still reluctant about placing an order? Our 100% Moneyback Guarantee backs you up on rare occasions where you aren’t satisfied with the writing. #### Order Tracking You don’t have to wait for an update for hours; you can track the progress of your order any time you want. We share the status after each step. #### Areas of Expertise Although you can leverage our expertise for any writing task, we have a knack for creating flawless papers for the following document types. # Trusted Partner of 9650+ Students for Writing From brainstorming your paper's outline to perfecting its grammar, we perform every step carefully to make your paper worthy of A grade. ##### Preferred Writer Hire your preferred writer anytime. Simply specify if you want your preferred expert to write your paper and we’ll make that happen. ##### Grammar Check Report Get an elaborate and authentic grammar check report with your work to have the grammar goodness sealed in your document. ##### One Page Summary You can purchase this feature if you want our writers to sum up your paper in the form of a concise and well-articulated summary. ##### Plagiarism Report You don’t have to worry about plagiarism anymore. Get a plagiarism report to certify the uniqueness of your work. ## Free Features$66FREE

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