# Mathematics Assignment | Custom Assignment Help

1. It’s a common idea that problems which contain only numbers are easy. This problem only deals with specific numbers, and it isn’t easy. The last digit of the number 5432178 is 8. The last two digits of that number are 7 and 8. What are the last 300 digits of  (300!)300 ? To put the problem into English: Take the factorial of the number 300, raise it to the 300th power and find the rightmost 300 digits. A direct approach will not work here. Wolfram Alpha will not be of much help. (See for yourself:  You need to carefully think about this one. HINT: Math should be fun. Play around with various smaller versions of the problem. See what happens. There is a pattern to discover.

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2. There are 170 students in this class. There are 254 seats, as limited by the fire code.In how many ways can we fill the classroom? Let’s say that it takes us one minute to reseat ourselves, that we will never repeat a seating arrangement, that a year has exactly 52 weeks and that we will be doing this for three hours a week.How many years would it take for us to try out all of the possible seating arrangements?

3. Imagine that ten people in the class got sick with the cold. Further eight got a flu. One person caught malaria, somehow. Ten people dropped the class. Another six are just plain sick of the class. Finally, one last student became a “Crown Stewardand Bailiff of the Chiltern Hundreds” in the United Kingdom and had to leave Canada. Suffice to say, none of those people will be attending. How does this level of attrition change the answer to the previous question? How many years will it take now to try out all seating arrangements

4. Let’s say that a company requires their employees to adhere to the following rules when it comes to choosing their password

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1. The first character has to an uppercase letter.

2. The fourth character has to be a lowercase letter.

3. The remaining six characters can be uppercase letters, lowercase letters or digits.

4. Let’s say that a hacker is attacking your email password. Thankfully they don’t have

information they have is this:

1. The password can have uppercase letters, lower case letters and digits.

2. The password is six to eight characters long, ends inclusive.

Given a computer that can try 1 billion (109) passwords per second, how long will it take to try out all of the passwords that the hacker considers possible? How much easier would the hacker’s job be if they had complete/correct information about the rules of the passwords? HINT: Split this into three sub-problems and combine the answers.

6. You are preparing soup for the whole family. You have 10 skirrets, 15 tomatoes, N onions and 3 cabbages. Dad must have a cabbage, but is otherwise not picky. Mom hates tomatoes, so she won’t have any of those. Granny dislikes skirrets, tomatoesand cabbages. You can eat anything. In how many ways can you prepare dinner for the four people in question, by distributing the veggies? You must give at minimum of one food item to everyone. How would the answer change if you had to give everyone at least two different vegetables?

7. Very broadly speaking, poker is a four-player game in which players draw five cards and win based on the content of this hand. In how many ways can a game of poker beginwithout anyone drawing a single card from the dead man’s hand? (The dead man’s hand is made out of two of the black eights, two of the black aces and of the queen of hearts.)

8. We often represent a musical scale as a sequence of 12 digits, either 0s or 1s. For a scale to be valid, the leading digit must be 1. 001100110011 is not a scale because it doesn’t start with a 1. 10 is not a scale, because it doesn’t have 12 digits. 120012001200 is not a scale because it uses digits other than 0 or 1. How many scales can exist in total?

A pentatonic scale is a scale which has 5 notes in it, this being represented by the five instances of the digit 1 being present in the symbol string that describes the scale.How many pentatonic scales can exist? Some scales won’t sound good if given to a novice musician. Those scales are called hemitonic and have two 1s adjacent to each other. (We can say that there is a ’run’ of two ’1’ digits present in such a scale.) How many pentatonic hemitonic scales can exist? How many pentatonic without this property exist? One thing that I have not told you earlier is that the first and the last digit are also considered adjacent. One way of thinking about scales is to arrange the digits in a circle.How does this knowledge change your answer to the hemitonic part of this question?Please note that there are many websites which answer this very question, from a musical theory viewpoint. However, those websites don’t consider some scales, by discarding scales which have large/long runs of 0s. (Such scales are hard to use musically even by experts, so that discard makes sense.) Please just do the work yourself, itis for the best.

9. The Polish national lottery is a draw of five numbers from a group of 49, without replacement. Matching three or more numbers allows you to buy another lottery ticket.What are the odd Get today

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